Journal articles on the topic 'Type-2 Fuzzy Systems Sliding Mode Control Lyapunov Approach State Observer'

This paper develops a new robust tracking control design for n-link robot manipulators with dynamic uncertainties, and unknown disturbances. The procedure is conducted by designing two adaptive interval type-2 fuzzy logic systems (AIT2-FLSs) to better approximate the parametric uncertainties on the system nominal. Then, in order to achieve the best tracking control performance and to enhance the system robustness against approximation errors and unknown disturbances, a new control algorithm, which uses a new synthesized AIT2 fuzzy sliding mode control (AIT2-FSMC) law, has been proposed. To deal with the chattering phenomenon without deteriorating the system robustness, the AIT2-FSMC has been designed so as to generate three adaptive control laws that provide the optimal gains value of the global control law. The adaptation laws have been designed in the sense of the Lyapunov stability theorem. Mathematical proof shows that the closed loop control system is globally asymptotically stable. Finally, a 2-link robot manipulator is used as case study to illustrate the effectiveness of the proposed control approach.

This paper presents a novel hybrid type-2 fuzzy sliding mode control approach for regulating active and reactive power exchanged with the utility grid by a doubly-fed induction generator in a wind energy conversion system. The main objective of this hybridization is to eliminate the steady-state chattering phenomenon inherent in sliding mode control while improving the transient delays caused by type-2 fuzzy controllers. In addition, the proposed control approach has proven to be successful in coping with varying generator parameters and exhibited good reference tracking. An in-depth comparative study with state-of-the-art advanced control techniques is also the focus of the present paper. The comparative study has three objectives, namely: a qualitative comparative study that aims to compare response times and reference tracking capabilities; a quantitative evaluation that takes into account time-integrated performance criteria; and finally, robustness capabilities. The simulation results, carried out in the Matlab/Simulink environment, have demonstrated the effectiveness and best performance of the proposed hybrid type-2 fuzzy sliding mode control with respect to other advanced techniques included in the comparison study.

To strengthen the overall control capability of the permanent magnet synchronous motor (PMSM) system, an improved non-singular fast terminal sliding-mode control strategy is proposed, that can simultaneously improve the shortcomings of traditional PI and sliding mode control (SMC), which include a large overshoot, large jitter, and poor robustness. First, a new type of non-singular fast terminal sliding-mode surface was constructed according to a surface-mounted PMSM, which avoids singular phenomena in the system. An improved power-reaching law was designed, which not only enables the control system to quickly approach the error to zero, but can also better suppress the chattering phenomenon. Moreover, an adaptive law is introduced to regulate the reaching law coefficient in real time, which further increases the control precision. The system stability was proven using the Lyapunov stability theory. Second, a beat-free predictive current controller was designed for the current loop to further strengthen the system's dynamic response. The matching disturbance of the extended state observer (ESO) is subsequently introduced, and the observed value is transmitted to the designed speed controller in real time. The advantages of the proposed strategy were analyzed through simulations, and its reliability was verified experimentally. Finally, through the simulation and experimental results, it was concluded that the improved non-singular fast terminal sliding mode control (INFTSMC) strategy for PMSM systems can overcome the shortcomings of traditional PI and sliding-mode control systems and increase the response speed and anti-interference ability of the system.

In this study, we develop a rigorous tracking control approach for quadrotor unmanned aerial vehicles (UAVs) with unknown dynamics, unknown physical parameters, and subject to unknown and unpredictable disturbances. In order to better estimate the unknown functions, seven interval type-2-adaptive fuzzy systems (IT2-AFSs) and five adaptive systems are designed. Then, a new IT2 adaptive fuzzy reaching sliding mode system (IT2-AFRSMS) which generates an optimal smooth adaptive fuzzy reaching sliding mode control law (AFRSMCL) using IT2-AFSs is introduced. The AFRSMCL is designed a way that ensures that its gains are efficiently estimated. Thus, the global proposed control law can effectively achieve the predetermined performances of the tracking control while simultaneously avoiding the chattering phenomenon, despite the approximation errors and all disturbances acting on the quadrotor dynamics. The adaptation laws are designed by utilizing the stability analysis of Lyapunov. A simulation example is used to validate the robustness and effectiveness of the proposed method of control. The obtained results confirm the results of the mathematical analysis in guaranteeing the tracking convergence and stability of the closed loop dynamics despite the unknown dynamics, unknown disturbances, and unknown physical parameters of the controlled system.

A novel interval type-2 intuition fuzzy brain emotional learning network model (IT2IFBELC) which depends only on the input and output data is proposed for the rehabilitation robot, which is different from model-based control algorithms that require exact dynamic model knowledge of the rehabilitation robot. The proposed model takes advantage of the type-2 intuition fuzzy theory and brain emotional neural network, and this is no rule initially; then, the structure and parameters of IT2IFBELC are tuned online simultaneously by the gradient approach and Lyapunov function. The system input data streams are directly imported into the neural network through an interval type-2 intuition fuzzy inference system (IT2IFIS), and then the results are subsequently piped into sensory and emotional channels which jointly produce the final outputs of the network. That is, the whole controller is composed of three parts, including the ideal sliding mode controller, the interval type-2 intuition fuzzy brain emotional learning network controller, and a powerful robust compensation controller, and then one Lyapunov function is designed to guarantee the rapid convergence of the control systems. For further illustrating the superiority of this model, several models are studied here for comparison, and the results show that the interval type-2 intuition fuzzy brain emotional learning network model can obtain better satisfactory control performance and be suitable to deal with the influence of the uncertainty of the rehabilitation robot.

SummaryThis paper addresses the systematic approach to design formation control for kinematic model of unicycle-type nonholonomic mobile robots. These robots are difficult to stabilize and control due to their nonintegrable constraints. The difficulty of control increases when there is a requirement to control a cluster of nonholonomic mobile robots in specific formation. In this paper, the design of the control scheme is presented in a three-step process. First, a robust state-feedback point-to-point stabilization control is designed using sliding mode control. In the second step, the controller is modified so as to address the tracking problem for time-varying reference trajectories. The proposed control scheme is shown to provide the desired robustness properties in the presence of the parameter variation, in the region of interest. Finally, in third step, tracking problem of a single nonholonomic mobile robot extends to formation control for a group of mobile robots in the leader–follower scenario using integral terminal- based sliding mode control augmented with stabilizing control. Starting with the transformation of the mathematical model of robots, the proposed controller ensures that the robots maintain a constant distance between each other to avoid collision. The main problem with the proposed controller is that it requires all states specially velocities. Therefore, the state-feedback control scheme is then extended to output feedback by incorporating a highgain observer. With the help of Lyapunov analysis and appropriate simulations, it is shown that the proposed output-feedback control scheme achieves the required control objectives. Furthermore, the closed loop system trajectories reach to desired equilibrium point in finite time while maintaining the special pattern.

This article presents a new design method of energy management strategy with model-free DC-Bus voltage control for the fuel-cell/battery/supercapacitor hybrid electric vehicle (FCHEV) system to enhance the power performance, fuel consumption, and fuel cell lifetime by considering regulation of DC-bus voltage. First, an efficient frequency-separating based-energy management strategy (EMS) is designed using Harr wavelet transform (HWT), adaptive low-pass filter, and interval type–2 fuzzy controller (IT2FC) to determine the appropriate power distribution for different power sources. Second, the ultra-local model (ULM) is introduced to re-formulate the FCHEV system by the knowledge of the input and output signals. Then, a novel adaptive model-free integral terminal sliding mode control (AMFITSMC) based on nonlinear disturbance observer (NDO) is proposed to force the actual values of the DC-link bus voltage and the power source’s currents track their obtained reference trajectories, wherein the NDO is used to approximate the unknown dynamics of the ULM. Moreover, the Lyapunov theorem is used to verify the stability of AMFITSMC via a closed-loop system. Finally, the FCHEV system with the presented method is modeled on a Matlab/Simulink environment, and different driving schedules like WLTP, UDDS, and HWFET driving cycles are utilized for investigation. The corresponding simulation results show that the proposed technique provides better results than the other methods, such as operational mode strategy and fuzzy logic control, in terms of the reduction of fuel consumption and fuel cell power fluctuations.

The use of assistive devices to control the loss of strength and range of motion of hemiplegic patients is becoming common. It is difficult to develop a precise control approach for a knee orthosis system because of the unpredictability of the dynamics and the unwanted subject’s spasm, jerk, and vibration during gait assistance. In this study, an adaptive neuro-fuzzy inference system (ANFIS) control system based on a nonlinear disturbance observer (NDO) and dynamic sliding mode controller (DSMC) is presented to restore the natural gait of hemiplegic patients experiencing mobility disorder and strength loss as well as monitor patient-induced disturbances and parameter variations during semiactive assistance of both the stance and swing phases. The knee orthosis system’s nonlinear dynamic relations are first developed using the Euler–Lagrange formation. Using MATLAB/Simulink, the dynamic model and controller design for the knee orthosis system was created. The Lyapunov theory is then used to ensure the knee orthosis system is asymptotically stable in view of the proposed controller once the proposed control scheme has been designed. The proposed control scheme’s (ANFIS–NDO–DSMC) gait tracking performances are shown and contrasted with the conventional sliding mode controller (SMC). Furthermore, a comparative performance analysis for parametric uncertainties and disturbances is presented to look at the robustness of the proposed controller (ANFIS–NDO–DSMC). The coefficient of determination ( R 2 ) and root mean square error (RMSE) between the reference knee angle and ANFIS–NDO–DSMC for stance phase are 1 and 0.000516 rad, respectively. For swing phase, R 2 and RMSE are 0.9999 and 0.003202 rad, respectively. For SMC, RMSE is 0.000643 and 0.003252 rad for stance and swing phases, respectively. Stance and swing phase R 2 is 0.9997 and 0.9994, respectively. As seen from simulation results, the proposed controller exhibited excellent gait tracking performance for the knee orthosis control with high robustness and very fast convergence to a steady state compared to SMC.

Introduction. Budget constraints in a world ravenous for electrical power have led utility companies to operate generating stations with full power and sometimes at the limit of stability. In such drastic conditions the occurrence of any contingency or disturbance may lead to a critical situation starting with poorly damped oscillations followed by loss of synchronism and power system instability. In the past decades, the utilization of supplementary excitation control signals for improving power system stability has received much attention. Power system stabilizers (PSS) are used to generate supplementary control signals for the excitation system in order to damp low-frequency oscillations caused by load disturbances or short-circuit faults. Problem. Adaptive power system stabilizers have been proposed to adequately deal with a wide range of operating conditions, but they suffer from the major drawback of requiring parameter model identification, state observation and on-line feedback gain computation. Power systems are nonlinear systems, with configurations and parameters that fluctuate with time that which require a fully nonlinear model and an adaptive control scheme for a practical operating environment. A new nonlinear adaptive fuzzy approach based on synergetic control theory which has been developed for nonlinear power system stabilizers to overcome above mentioned problems. Aim. Synergetic control theory has been successfully applied in the design of power system stabilizers is a most promising robust control technique relying on the same principle of invariance found in sliding mode control, but without its chattering drawback. In most of its applications, synergetic control law was designed based on an asymptotic stability analysis and the system trajectories evolve to a specified attractor reaching the equilibrium in an infinite time. In this paper an indirect finite time adaptive fuzzy synergetic power system stabilizer for damping local and inter-area modes of oscillations for power systems is presented. Methodology. The proposed controller design is based on an adaptive fuzzy control combining a synergetic control theory with a finite-time attractor and Lyapunov synthesis. Enhancing existing adaptive fuzzy synergetic power system stabilizer, where fuzzy systems are used to approximate unknown system dynamics and robust synergetic control for only providing asymptotic stability of the closed-loop system, the proposed technique procures finite time convergence property in the derivation of the continuous synergetic control law. Analytical proofs for finite time convergence are presented confirming that the proposed adaptive scheme can guarantee that system signals are bounded and finite time stability obtained. Results. The performance of the proposed stabilizer is evaluated for a single machine infinite bus system and for a multi machine power system under different type of disturbances. Simulation results are compared to those obtained with a conventional adaptive fuzzy synergetic controller.

<strong><em>Introduction.&nbsp;</em></strong><em>Budget constraints in a world ravenous for electrical power have led utility companies to operate generating stations with full power and sometimes at the limit of stability. In such drastic conditions the occurrence of any contingency or disturbance may lead to a critical situation starting with poorly damped oscillations followed by loss of synchronism and power system instability. In the past decades, the utilization of supplementary excitation control signals for improving power system stability has received much attention. Power system stabilizers (PSS) are used to generate supplementary control signals for the excitation system in order to damp low-frequency oscillations caused by load disturbances or short-circuit faults<strong>. Problem.&nbsp;</strong>Adaptive power system stabilizers have been proposed to adequately deal with a wide range of operating conditions, but they suffer from the major drawback of requiring parameter model identification, state observation and on-line feedback gain computation. Power systems are nonlinear systems, with configurations and parameters that fluctuate with time that which require a fully nonlinear model and an adaptive control scheme for a practical operating environment. A new nonlinear adaptive fuzzy approach based on synergetic control theory which has been developed for nonlinear power system stabilizers to overcome above mentioned problems<strong>. Aim.</strong>&nbsp;Synergetic control theory has been successfully applied in the design of power system stabilizers is a most promising robust control technique relying on the same principle of invariance found in sliding mode control, but without its chattering drawback. In most of its applications, synergetic control law was designed based on an asymptotic stability analysis and the system trajectories evolve to a specified attractor reaching the equilibrium in an infinite time. In this paper an indirect finite time adaptive fuzzy synergetic power system stabilizer for damping local and inter-area modes of oscillations for power systems is presented.&nbsp;<strong>Methodology.</strong>&nbsp;The proposed controller design is based on an adaptive fuzzy control combining a synergetic control theory with a finite-time attractor and Lyapunov synthesis. Enhancing existing adaptive fuzzy synergetic power system stabilizer, where fuzzy systems are used to approximate unknown system dynamics and robust synergetic control for only providing asymptotic stability of the closed-loop system, the proposed technique procures finite time convergence property in the derivation of the continuous synergetic control law. Analytical proofs for finite time convergence are presented confirming that the proposed adaptive scheme can guarantee that system signals are bounded and finite time stability obtained.</em><em>&nbsp;<strong>Results.</strong>&nbsp;The performance of the proposed stabilizer is evaluated for a single machine infinite bus system and for a multi machine power system under different type of disturbances. Simulation results are compared to those obtained with a conventional adaptive fuzzy synergetic controller.</em>

The Third International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment, and Management (HNICEM) was held in Century Park Hotel, Manila, Philippines from March 15 to 18, 2007. The theme on this conference was Technology Creativity and Innovations for Economic Development. As has been done from the previous HNICEM conferences, cutting edge papers presented from this conference are reviewed and selected for JACIII special issue publication. In this special issue, 10 articles are selected that will provide valuable references for researchers and practitioners. The first article presents an integrated algorithm that provides a mobile robot the ability to plan an optimal path and does online collision avoidance in a totally unknown environment. The second article presents a fuzzy controller technique in navigation with obstacle avoidance for a general purpose mobile robot in a given global environment with image processing technique using Open Source Computer Vision. The third article presents a model-based controller for helicopter using the sliding mode approach. The controller assumes that only measured outputs are available and it uses sliding mode observer to estimate the state of the system. The fourth article presents a real-time fuzzy logic based parallel parking system in an FPGA platform. The fifth article presents performance analysis of container unloading operations using simplified analytical model (SAM). The sixth article presents a neuro-fuzzy approach with additional moving average window data filter and fuzzy clustering algorithm use to forecast electrical load. The seventh article presents a new design and implementation of a multi-output fuzzy controller for real time control which utilizes lesser memory and executes faster than an existing type of multiple single-output fuzzy logic controllers. The eight article presents a new method based on multi-objective evolutionary algorithms to evolve low complexity neural controllers that allows an agent to perform two different tasks simultaneously. The ninth and tenth articles present genetic networks programming for stock market trading rules and for traffic systems applications, respectively. We extend our warmest thanks and deepest gratitude to the distinguished authors and reviewers who have contributed to this special issue for their outstanding contributions and cooperation. We are also grateful to Prof. Toshio Fukuda and Prof. Kaoru Hirota, chief editors of JACIII, for their continued support to all the HINICEM International Conferences. Come March 12 to 15, 2009, the 4th HNICEM International Conference will be held in Manila, Philippines. We thank the IEEE Philippines for its continuing sponsorship. Also to JACIII journal, as outstanding papers presented in this conference will be selected for publication in a special issue. We invite you to submit your research papers and to participate in HNICEM 2009. For further information, please visit “http://www.dlsu.edu.ph/conferences/hnicem/”.

In this paper we propose to develop an adaptive type-2 fuzzy robust controller with a stat observer to control a robotic system. For this, we the approximate the system with two type-2 fuzzy systems. To overcome the problem of the state measures, we propose a state observer allowing to converge quickly to the real values and hence guarantees the stability of the closed loop system. The robustness of the closed loop system is ensured by using a modified sliding mode control, where the chattering phenomenon are removed. Simulation results are given to show the efficiency of the proposed approach. &nbsp;

The issue of non-fragile observer-based adaptive integral sliding mode control for a class of Takagi–Sugeno (T-S) fuzzy descriptor systems with uncertainties and unmeasurable premise variables is investigated. General nonlinear systems are represented by nonlinear T-S fuzzy descriptor models, because premise variables depend on unmeasurable system states and fuzzy models have different derivative matrices. By introducing the system state derivative as an auxiliary state vector, original fuzzy descriptor systems are transformed into augmented systems for which system properties remain the same. First, a novel integral sliding surface, which includes estimated states of the sliding mode observer and controller gain matrices, is designed to obtain estimation error dynamics and sliding mode dynamics. Then, some sufficient linear matrix inequality (LMI) conditions for designing the observer and the controller gains are derived using the appropriate fuzzy Lyapunov functions and Lyapunov theory. This approach yields asymptotically stable sliding mode dynamics. Corresponding auxiliary variables are introduced, and the Finsler's lemma is employed to eliminate coupling of controller gain matrices, observer gain matrices, Lyapunov function matrices, and/or observer gain perturbations. An observer-based integral sliding mode control strategy is obtained to assure that reachability conditions are satisfied. Moreover, a non-fragile observer and a non-fragile adaptive controller are developed to compensate for system uncertainties and perturbations in both the observer and the controller. Finally, example results are presented to illustrate the effectiveness and merits of the proposed method.

&lt;p style='text-indent:20px;'&gt;This paper discusses the problem of stabilization of interval type-2 fuzzy systems with uncertainties, time delay and external disturbance using a dynamic sliding mode controller. The sliding surface function, which is based on both the system's state and control input vectors, is used during the control design process. The sliding mode dynamics are presented by defining a new vector that augments the system state and control vectors. First, the reachability of the addressed sliding mode surface is demonstrated. Second, the required sufficient conditions for the system's stability and the proposed control design are derived by using extended dissipative theory and an asymmetric Lyapunov-Krasovskii functional approach. Unlike some existing sliding mode control designs, the one proposed in this paper does not require the control coefficient matrices of all linear subsystems to be the same, reducing the method's conservatism. Finally, numerical examples are provided to demonstrate the viability and superiority of the proposed design method.&lt;/p&gt;

Abstract This paper focuses on the tracking and synchronization control of multi-motor systems and proposes an adaptive fuzzy sliding mode control approach based on an extended state observer. First, a nonsingular sliding mode controller is designed by using the coupling error of multi-motor systems, ensuring that the error converges to a smaller region within a fixed time. Second, fuzzy logic system takes the role of the control signal's discontinuous switching term, which allows the system to adaptively modify its parameters and successfully lessen chattering. Finally, to handle the system's inherent uncertainties and external disturbances, an extended state observer is constructed and integrated into the controller, with its stability proven via the Lyapunov function.Comparative experiments demonstrate that the proposed controller outperforms traditional controllers in terms of control accuracy and response speed.

Abstract This work addresses the problem of sliding mode control (SMC) design for a continuous-time non-linear stochastic system with Levy-type noise. A state observer model is constructed to estimate the unavailable state information. Furthermore, Levy-type noise is considered to analyse small perturbations and to characterize the appearance of large samples that will occur in the system. Lyapunov stability and SMC theory are used to provide some sufficient conditions that ensure the stochastic stability of the error system and reachability of the predefined sliding surface. Finally, an example is given to demonstrate the feasibility of the proposed approach.

In this paper, an active fault-tolerance controller is proposed for a two-degree-of-freedom (2-DOF) helicopter model with different types of sensor faults. The proposed controller is designed by combining an interval type-2 fuzzy logic control approach with a sliding-mode control technique. In addition, the controller is compensated by a sliding-mode observer used to estimate faults in real-time. For the proposed control scheme, the overall stability of the closed-loop system is proven using the Lyapunov stability theory. Finally, numerical simulations and experiments verify that the proposed scheme achieves superior control performance in the case of sensor failure.

AbstractThis study formulates the unified fault reconstruction and fault‐tolerant tracking (FTT) control framework for the cyber‐physical (C‐P) systems subject to time‐varying actuator faults, nonlinearity, and deception attacks. Primarily, the interval type‐2 fuzzy (IT2‐F) process efficiently approximates the nonlinear C‐P systems. Further, the unknown actuator faults are proficiently reconstructed through IT2‐F‐based sliding mode (SM) observer technique. Then, the active FTT control strategy is utilized in this work to stabilize the tracking error system. Precisely, the reference system is designated by means of IT2‐F approach. To represent the deception attacks, the Bernoulli random variable is employed in the planned controller. In a nutshell, the proposed SM observer‐based FTT control assures satisfactory tracking outcomes of the examined systems notwithstanding the presence of deception attacks and unknown actuator faults. As well, the Lyapunov stability concept is applied in this study to acquire the stability conditions in the form of linear matrix inequalities. Following this, the two numerical simulations are illustrated to exemplify the conceptual as well as the practical importance of the proposed method.

This paper investigates the challenging problem of fixed time trajectory tracking for robotic manipulators under the presence of unavailable model perturbation, external disturbance and from different initial states. Firstly, a novel fixed-time extended state observer (FESO) is designed to estimate and compensate the lumped disturbance, which is analyzed and proved to be stable in the sense of fixed time bounded stability. Secondly, a new type of fixed-time prescribed performance control (FPPC) is constructed to guarantee the system convergences to stable state within a predefined time and enhance transient performance. Furthermore, a novel continuous fixed time nonsingular fast terminal sliding mode variable is established, which addresses singularity obstacle in terminal sliding mode. Together with FESO and FPPC, a new fixed-time adaptive nonsingular fast terminal sliding mode controller (FANFTSMC) is developed. Meanwhile, an adaptive terminal sliding mode reaching law adopted in FANFTSMC promotes the robustness and decreases the chattering phenomenon. Then, the Lyapunov approach is given to clarify the advantages of FANFTSMC in terms of predefined time stabilization and which is demonstrated on a 2-DOF robotic manipulators. Thirdly, theoretical analysis and experiments are presented to illustrate the formulated control strategy owns fine performance and stronger robustness.

This paper introduces a novel method for controlling a surface permanent magnet synchronous motor (SPMSM) during demagnetization fault conditions. The proposed fault-tolerant control (FTC) system incorporates a combination of a fuzzy extended state observer (FESO) based on an interval type 2 fuzzy logic controller (IT2FLC) and second-order sliding mode control (SOSMC) utilizing the super-twisting algorithm. The FESO aims to identify and eliminate demagnetization faults through reconstruction control. The FTC system enhances the dynamic performance and disturbance rejection of the SPMSM, providing a robust solution in the event of a demagnetization fault.

This paper investigates the observer-based resilient sliding mode control problem for cyber-physical systems (CPSs). In multiple transmission channels under aperiodic denial-of-service (DoS) attacks, a decentralized dynamic event-triggering scheme is designed to reduce the network transmission burden. To construct such a periodically sampled event-triggering scheme, a set of finite-time observers is designed to obtain estimated system states. On the controller side, to obtain higher control reliability under DoS attacks, decentralized observers are correspondingly arranged in these channels. In this process, an exponential stability condition is obtained using a piecewise Lyapunov–Krasovskii functional approach. The stability conditions of linear matrix inequalities (LMIs) are given, and the computational complexity is much less compared with the counterparts in some existing results for multiple channels. To further improve the disturbance rejection performance, a weighed integral-type sliding surface is introduced, and the impact of unreliable state estimating channels is reduced. An auxiliary system is also designed to handle the input saturation, and the closed-loop system under DoS attacks is asymptotically stable. Finally, an example of an unmanned aerial vehicle is given to verify the effectiveness of the obtained resilient control approach.

SummaryThis study investigates the issue of containment control (CC) of multi‐agent systems (MASs) that are heterogeneous, nonlinear, and fractional‐order while taking practical scenarios into account, such as uncertainties, unknown nonlinearities, time‐varying state delays, and distributed time‐varying delays. A fully distributed adaptive observer is created for each follower in accordance with the communication topology information among agents. This observer is designed to estimate the convex combination information of the leaders. The approach utilizes interval type‐2 fuzzy set theory and adaptive methods to design a distributed containment control strategy that only uses the self‐information of the followers and neighbor nodes' information. Sufficient conditions for implementing containment control are given. A new Lyapunov‐Krasovskii functional (LKF) is constructed, and the stability of the system with feedback loop is proven using fractional‐order theory and inequality methods. Lastly, a simulation example is presented to illustrate the efficacy of the proposed approach.

This paper introduces a new saturated robust control technique for quadrotor aircraft modeled by second-order Ordinary Differential Equations (ODEs), considering disturbances in the control channel (matched disturbances). The control design employs a Sliding Mode Control (SMC) approach, featuring in: (i) a novel saturated homogeneous sliding manifold, (ii) a novel tracking controller, namely, Bounded Robust Finite-Time Homogeneous Sliding Mode Control (BRFTHSMC). An Improved Fixed-time Convergent Extended State Observer (IFCESO) is incorporated into the control scheme to handle disturbances. Together the BRFTHSMC and the IFCESO establish a reliable Active Disturbance Rejection Control (ADRC) framework. The latter ensures finite-time convergence of the errors quantities to the origin along with effective disturbance rejection. Rigorous stability analysis is conducted based on Lyapunov theory. Beside control design, another distinguishing theoretical outcome of this paper in the form of Corollary is the extension of the present results to integrator-type systems (higher-order systems). The study is substantiated through MATLAB®/Simulink simulations and Robot Operating System (ROS)/Gazebo implementation, validating the theoretical foundation. Extensive experimental tests on real hardware, including attitude and Cartesian trajectory tracking under various disturbances, further affirm the theoretical findings. The synthesized control system surpasses alternative methods in terms of control signal’s boundedness, finite-time tracking stability, transient response performance, and steady-state precision. Notably, the control input circumvents singularity challenges observed in conventional SMC approaches. In addition to trajectory tracking experiments, the controller’s effectiveness is demonstrated in real-world search and rescue scenarios. Therefore, a Deep Neural Network (DNN) algorithm, based on a MS COCO-pretrained Single Shot Detector (SSD-Mobilenet-v2), is employed for a person detection mission in an unknown search area.

The design of a new control approach for the longitudinal motion of the Cessna Citation X during cruise is performed using a combination of sliding mode control (SMC) system, type 1 fuzzy logic system, and adaptive control system. This methodology is presented for 1) controlling the aircraft pitch rate and 2) stabilizing the aircraft speed during turbulence. The nonlinear model of the aircraft was generated using a simulation platform, which was designed based on flight data obtained from the highest Federal Aviation Administration–certified Level-D Research Aircraft Flight Simulator. The type 1 adaptive fuzzy logic system was implemented to approximate unknown functions for constructing the equivalent part of the SMC system that handled the effects of uncertainties and turbulence. The adaptation laws, derived from the Lyapunov theorem, were used to update the approximated functions in the control law at each flight condition and simulation iteration. Using the control systems combination, the pitch rate could follow the given reference signal, while the aircraft speed remained at a reference value with and without turbulence across the whole flight envelope. Results have shown that the proposed controllers satisfied tracking performance while generating smooth elevator deflection, both of which are important for real-aircraft applications.

PurposeA distinctive feature of tilt-rotor UAVs is that they can be fully actuated, whereas in fixed-angle rotor UAVs (e.g. common-type quadrotors, octorotors, etc.), the associated dynamic model is characterized by underactuation. Because of the existence of more control inputs, in tilt-rotor UAVs, there is more flexibility in the solution of the associated nonlinear control problem. On the other side, the dynamic model of the tilt-rotor UAVs remains nonlinear and multivariable and this imposes difficulty in the drone's controller design. This paper aims to achieve simultaneously precise tracking of trajectories and minimization of energy dissipation by the UAV's rotors. To this end elaborated control methods have to be developed.Design/methodology/approachA solution of the nonlinear control problem of tilt-rotor UAVs is attempted using a novel nonlinear optimal control method. This method is characterized by computational simplicity, clear implementation stages and proven global stability properties. At the first stage, approximate linearization is performed on the dynamic model of the tilt-rotor UAV with the use of first-order Taylor series expansion and through the computation of the system's Jacobian matrices. This linearization process is carried out at each sampling instance, around a temporary operating point which is defined by the present value of the tilt-rotor UAV's state vector and by the last sampled value of the control inputs vector. At the second stage, an H-infinity stabilizing controller is designed for the approximately linearized model of the tilt-rotor UAV. To find the feedback gains of the controller, an algebraic Riccati equation is repetitively solved, at each time-step of the control method. Lyapunov stability analysis is used to prove the global stability properties of the control scheme. Moreover, the H-infinity Kalman filter is used as a robust observer so as to enable state estimation-based control. The paper's nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, the nonlinear optimal control approach for UAVs with tilting rotors is compared against flatness-based control in successive loops, with the latter method to be also exhibiting satisfactory performance.FindingsSo far, nonlinear model predictive control (NMPC) methods have been of questionable performance in treating the nonlinear optimal control problem for tilt-rotor UAVs because NMPC's convergence to optimum depends often on the empirical selection of parameters while also lacking a global stability proof. In the present paper, a novel nonlinear optimal control method is proposed for solving the nonlinear optimal control problem of tilt rotor UAVs. Firstly, by following the assumption of small tilting angles, the state-space model of the UAV is formulated and conditions of differential flatness are given about it. Next, to implement the nonlinear optimal control method, the dynamic model of the tilt-rotor UAV undergoes approximate linearization at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. The linearization process is based on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms from the Taylor series, is considered to be a perturbation that is asymptotically compensated by the robustness of the control scheme. For the linearized model of the UAV, an H-infinity stabilizing feedback controller is designed. To select the feedback gains of the H-infinity controller, an algebraic Riccati equation has to be repetitively solved at each time-step of the control method. The stability properties of the control scheme are analysed with the Lyapunov method.Research limitations/implicationsThere are no research limitations in the nonlinear optimal control method for tilt-rotor UAVs. The proposed nonlinear optimal control method achieves fast and accurate tracking of setpoints by all state variables of the tilt-rotor UAV under moderate variations of the control inputs. Compared to past approaches for treating the nonlinear optimal (H-infinity) control problem, the paper's approach is applicable also to dynamical systems which have a non-constant control inputs gain matrix. Furthermore, it uses a new Riccati equation to compute the controller's gains and follows a novel Lyapunov analysis to prove global stability for the control loop.Practical implicationsThere are no practical implications in the application of the nonlinear optimal control method for tilt-rotor UAVs. On the contrary, the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed to the linear parameter varying (LPV) form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. The stability properties of the Galerkin series expansion-based optimal control approaches are still unproven.Social implicationsThe proposed nonlinear optimal control method is suitable for using in various types of robots, including robotic manipulators and autonomous vehicles. By treating nonlinear control problems for complicated robotic systems, the proposed nonlinear optimal control method can have a positive impact towards economic development. So far the method has been used successfully in (1) industrial robotics: robotic manipulators and networked robotic systems. One can note applications to fully actuated robotic manipulators, redundant manipulators, underactuated manipulators, cranes and load handling systems, time-delayed robotic systems, closed kinematic chain manipulators, flexible-link manipulators and micromanipulators and (2) transportation systems: autonomous vehicles and mobile robots. Besides, one can note applications to two-wheel and unicycle-type vehicles, four-wheel drive vehicles, four-wheel steering vehicles, articulated vehicles, truck and trailer systems, unmanned aerial vehicles, unmanned surface vessels, autonomous underwater vessels and underactuated vessels.Originality/valueThe proposed nonlinear optimal control method is a novel and genuine result and is used for the first time in the dynamic model of tilt-rotor UAVs. The nonlinear optimal control approach exhibits advantages against other control schemes one could have considered for the tilt-rotor UAV dynamics. For instance, (1) compared to the global linearization-based control schemes (such as Lie algebra-based control or flatness-based control), it does not require complicated changes of state variables (diffeomorphisms) and transformation of the system's state-space description. Consequently, it also avoids inverse transformations which may come against singularity problems, (2) compared to NMPC, the proposed nonlinear optimal control method is of proven global stability and the convergence of its iterative search for an optimum does not depend on initialization and controller's parametrization, (3) compared to sliding-mode control and backstepping control the application of the nonlinear optimal control method is not constrained into dynamical systems of a specific state-space form. It is known that unless the controlled system is found in the input–output linearized form, the definition of the associated sliding surfaces is an empirical procedure. Besides, unless the controlled system is found in the backstepping integral (triangular) form, the application of backstepping control is not possible, (4) compared to PID control, the nonlinear optimal control method is of proven global stability and its performance is not dependent on heuristics-based selection of parameters of the controller and (5) compared to multiple-model-based optimal control, the nonlinear optimal control method requires the computation of only one linearization point and the solution of only one Riccati equation.

Purpose To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1 are often used in the joints of a robotic manipulator. This results into an actuator with large mechanical impedance (also known as nonback-drivable actuator). This in turn generates high contact forces when collision of the robotic mechanism occur and can cause humans’ injury. Another disadvantage of electric actuators is that they can exhibit overheating when constant torques have to be provided. Comparing to electric actuators, pneumatic actuators have promising properties for robotic applications, due to their low weight, simple mechanical design, low cost and good power-to-weight ratio. Electropneumatically actuated robots usually have better friction properties. Moreover, because of low mechanical impedance, pneumatic robots can provide moderate interaction forces which is important for robotic surgery and rehabilitation tasks. Pneumatic actuators are also well suited for exoskeleton robots. Actuation in exoskeletons should have a fast and accurate response. While electric motors come against high mechanical impedance and the risk of causing injuries, pneumatic actuators exhibit forces and torques which stay within moderate variation ranges. Besides, unlike direct current electric motors, pneumatic actuators have an improved weight-to-power ratio and avoid overheating problems. Design/methodology/approach The aim of this paper is to analyze a nonlinear optimal control method for electropneumatically actuated robots. A two-link robotic exoskeleton with electropneumatic actuators is considered as a case study. The associated nonlinear and multivariable state-space model is formulated and its differential flatness properties are proven. The dynamic model of the electropneumatic robot is linearized at each sampling instance with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Within each sampling period, the time-varying linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. An H-infinity controller is designed for the linearized model of the robot aiming at solving the related optimal control problem under model uncertainties and external perturbations. An algebraic Riccati equation is solved at each time-step of the control method to obtain the stabilizing feedback gains of the H-infinity controller. Through Lyapunov stability analysis, it is proven that the robot’s control scheme satisfies the H-infinity tracking performance conditions which indicate the robustness properties of the control method. Moreover, global asymptotic stability is proven for the control loop. The method achieves fast convergence of the robot’s state variables to the associated reference trajectories, and despite strong nonlinearities in the robot’s dynamics, it keeps moderate the variations of the control inputs. Findings In this paper, a novel solution has been proposed for the nonlinear optimal control problem of robotic exoskeletons with electropneumatic actuators. As a case study, the dynamic model of a two-link lower-limb robotic exoskeleton with electropneumatic actuators has been considered. The dynamic model of this robotic system undergoes first approximate linearization at each iteration of the control algorithm around a temporary operating point. Within each sampling period, this linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modeling error which is due to the truncation of higher-order terms from the Taylor series is considered to be a perturbation which is asymptotically compensated by the robustness of the control algorithm. To stabilize the dynamics of the electropneumatically actuated robot and to achieve precise tracking of reference setpoints, an H-infinity (optimal) feedback controller is designed. Actually, the proposed H-infinity controller for the model of the two-link electropneumatically actuated exoskeleton achieves the solution of the associated optimal control problem under model uncertainty and external disturbances. This controller implements a min-max differential game taking place between: (i) the control inputs which try to minimize a cost function which comprises a quadratic term of the state vector’s tracking error and (ii) the model uncertainty and perturbation inputs which try to maximize this cost function. To select the stabilizing feedback gains of this H-infinity controller, an algebraic Riccati equation is being repetitively solved at each time-step of the control method. The global stability properties of the H-infinity control scheme are proven through Lyapunov analysis. Research limitations/implications Pneumatic actuators are characterized by high nonlinearities which are due to air compressibility, thermodynamics and valves behavior and thus pneumatic robots require elaborated nonlinear control schemes to ensure their fast and precise positioning. Among the control methods which have been applied to pneumatic robots, one can distinguish differential geometric approaches (Lie algebra-based control, differential flatness theory-based control, nonlinear model predictive control [NMPC], sliding-mode control, backstepping control and multiple models-based fuzzy control). Treating nonlinearities and fault tolerance issues in the control problem of robotic manipulators with electropneumatic actuators has been a nontrivial task. Practical implications The novelty of the proposed control method is outlined as follows: preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics. These results considered that the control inputs gain matrix is not dependent on the values of the system’s state vector. Moreover, in these approaches the linearization was performed around points of the desirable trajectory, whereas in the present paper’s control method the linearization points are related with the value of the state vector at each sampling instance as well as with the last sampled value of the control inputs vector. The Riccati equation which has been proposed for computing the feedback gains of the controller is novel, so is the presented global stability proof through Lyapunov analysis. This paper’s scientific contribution is summarized as follows: (i) the presented nonlinear optimal control method has improved or equally satisfactory performance when compared against other nonlinear control schemes that one can consider for the dynamic model of robots with electropneumatic actuators (such as Lie algebra-based control, differential flatness theory-based control, nonlinear model-based predictive control, sliding-mode control and backstepping control), (ii) it achieves fast and accurate tracking of all reference setpoints, (iii) despite strong nonlinearities in the dynamic model of the robot, it keeps moderate the variations of the control inputs and (iv) unlike the aforementioned alternative control approaches, this paper’s method is the only one that achieves solution of the optimal control problem for electropneumatic robots. Social implications The use of electropneumatic actuation in robots exhibits certain advantages. These can be the improved weight-to-power ratio, the lower mechanical impedance and the avoidance of overheating. At the same time, precise positioning and accurate execution of tasks by electropneumatic robots requires the application of elaborated nonlinear control methods. In this paper, a new nonlinear optimal control method has been developed for electropneumatically actuated robots and has been specifically applied to the dynamic model of a two-link robotic exoskeleton. The benefit from using this paper’s results in industrial and biomedical applications is apparent. Originality/value A comparison of the proposed nonlinear optimal (H-infinity) control method against other linear and nonlinear control schemes for electropneumatically actuated robots shows the following: (1) Unlike global linearization-based control approaches, such as Lie algebra-based control and differential flatness theory-based control, the optimal control approach does not rely on complicated transformations (diffeomorphisms) of the system’s state variables. Besides, the computed control inputs are applied directly on the initial nonlinear model of the electropneumatic robot and not on its linearized equivalent. The inverse transformations which are met in global linearization-based control are avoided and consequently one does not come against the related singularity problems. (2) Unlike model predictive control (MPC) and NMPC, the proposed control method is of proven global stability. It is known that MPC is a linear control approach that if applied to the nonlinear dynamics of the electropneumatic robot, the stability of the control loop will be lost. Besides, in NMPC the convergence of its iterative search for an optimum depends on initialization and parameter values selection and consequently the global stability of this control method cannot be always assured. (3) Unlike sliding-mode control and backstepping control, the proposed optimal control method does not require the state-space description of the system to be found in a specific form. About sliding-mode control, it is known that when the controlled system is not found in the input-output linearized form the definition of the sliding surface can be an intuitive procedure. About backstepping control, it is known that it cannot be directly applied to a dynamical system if the related state-space model is not found in the triangular (backstepping integral) form. (4) Unlike PID control, the proposed nonlinear optimal control method is of proven global stability, the selection of the controller’s parameters does not rely on a heuristic tuning procedure, and the stability of the control loop is assured in the case of changes of operating points. (5) Unlike multiple local models-based control, the nonlinear optimal control method uses only one linearization point and needs the solution of only one Riccati equation so as to compute the stabilizing feedback gains of the controller. Consequently, in terms of computation load the proposed control method for the electropneumatic actuator’s dynamics is much more efficient.

International Journal on Bioinformatics &amp; Biosciences (IJBB) Vol.3, No.3, September 2013 DOI: 10.5121/ijbb.2013.3303 25 STRATEGY FOR ELECTROMYOGRAPHY BASED DIAGNOSIS OF NEUROMUSCULAR DISEASES FOR ASSISTIVE REHABILITATION Sailesh Conjeti1 and Bijay Kumar Rout2 1Department of Electrical and Electronics Engineering, Birla Institute of Technology and Science, Pilani, Rajasthan, India. 2Department of Mechanical Engineering, Birla Institute of Technology and Science, Pilani, Rajasthan, India. ABSTRACT Assistive Rehabilitation aims at developing procedures and therapies which reinstate lost body functions for individuals with disabilities. Researchers have monitored electrophysiological activity of muscles using biofeedback obtained from Electromyogram signals collected at appropriate innervation points. In this paper, we present a comprehensive technique for detection of neuromuscular disease in a subject and a strategy for continuous therapeutic assessment using the Rehabilitation Assessment Matrix. The decision making tool has been trained using a wide spectrum of synthetic physiological data incorporating varying degrees of myopathy and neuropathy from beginning stages to acute. The statistical, spectral and cepstral features extracted from EMG have been used to train a Cascade Correlation Neural Network Classifier for disease assessment. The diagnostic yield of the classifier is 91.2% accuracy, 85.3% specificity and 91.35% sensitivity. The strategy has also been extended to include isotonic contractions in addition to static isometric contractions. This comprehensive strategy is proposed to aid physicians plan and schedule treatment procedures to maximize the therapeutic value of the rehabilitation process. KEYWORDS Electromyography, Rehabilitation, Myopathy, Neuropathy and Cascade Correlation Neural Network. 1.INTRODUCTION Assistive Rehabilitation of affected individuals aims at restoring original body functionality by compensating for the lost functions and thus providing opportunities to lead an independent life. Such procedures for neuromuscular rehabilitation often require design of manipulative physiotherapy procedures, following the detection of neuromuscular disease (NMD) in the subject. The biofeedback acquired from the patient is crucial to the design and execution of an effective medical rehabilitation scheme [1]. A complete and comprehensive assessment is often labour-intensive and expensive because the design and configuration of individualistic procedures require training of highly-skilled physiotherapists with appropriate expert knowledge. In this situation, Computer Aided Diagnostics of NMDs helps minimize observer bias, facilitates inter-subject comparison and aids the physicians to arrive at a more accurate diagnosis [2]-[3]. Neuromuscular facilitation mechanisms for individuals affected with NMDs must be designed considering individual&rsquo;s neurophysiology, motor-learning and motor development functions [4]. This work primarily focuses on two classes of NMD viz. Myopathy and Neuropathy. Myopathy refers to a medical condition where muscle weakness is observed due to reduced functionality and activation of muscle fibres for a particular nervous stimulation. Muscle cramps, stiffness International Journal on Bioinformatics &amp; Biosciences (IJBB) Vol.3, No.3, September 2013 26 and spasm are the usual reported symptoms associated with myopathic disorders [5]. Neuropathy, on the other hand, is a neurogenic condition resulting in loss of movement and haptic sensation owing to nervous damage. The reported symptoms include nerve pain, partial or complete paralysis, abnormal sensations and muscle weakness [6]. The treatment of neuromuscular diseases varies from medications, physical therapy, splinting and in acute cases even surgery is suggested. The treatment is often administered on the basis of the cause and origin of NMDs and the degree of its severity. The presented work aims to develop an Electromyography based assessment approach for NMDs which is fast and reliable. The proposed methodologies would aid the physiotherapists in preparing an appropriate medical treatment scheme with proper scheduling of physiological exercise routines, thus maximizing the therapeutic value of the rehabilitation procedure instituted. Figure 1. Intramuscular EMG Recordings (a) Normal Subject (b) Neuropathic Subject and (c) Myopathic Subject 2. ELECTROMYOGRAPHY AND APPLICATIONS IN NEUROMUSCULAR DISEASE DIAGNOSIS Researchers in the field of health monitoring have used the Electromyogram (EMG) signal for detection and monitoring of NMDs as they are accessible as bioelectric signals under direct volitional control [7]. EMG is a cumulative effect of the motor unit action potentials (MUAPs), generated by the motor neurons, which are responsible for actuating the skeletal muscles for support and motion of the human skeleton [8]. Electromyography signals acquired from appropriate muscular regions reflect on the muscle&rsquo;s tone, strength, abnormalities in reflexes, ideomotor and voluntary movements and postural equilibrium reactions [9]. Figure 1 illustrates a typical intramuscular EMG recorded from three subjects (a) Healthy, (b) Neuropathy and (c) Myopathy (Figure adapted from [10]). Berzuini et al. investigated into the applicability of EMG signals collected from the right brachii muscles to detect neurogenic disorders. Variations observed in both time-domain and frequency domain parameters helped them to find topographical clusters in the multivariate space of EMG parameters corresponding to neuropathic subjects [11]. Pattiachis et al. investigated into applying Neural Network models of EMG diagnosis for detecting NMDs. They trained the networks using extracted morphological features of MUAP waveform after signal decomposition procedures on EMG [3]. These research works establish the suitability of EMG signals for detection of International Journal on Bioinformatics &amp; Biosciences (IJBB) Vol.3, No.3, September 2013 27 neuromuscular disease and development of a reliable rehabilitation strategy for a particular subject. 3. REHABILITATION ASSESSMENT MATRIX The current styles of rehabilitation assessment forms used by medical practitioners in Physical Medicine and Rehabilitation (PMR) documents the patient&rsquo;s strengths, abilities, preferences, needs, findings, and recommendations for treatment. Inferences drawn from these ensure that appropriate rehabilitation procedures are administered on timely basis [12]. The Rehabilitation Assessment Matrix (RAM) has been developed to meet the need for comprehensive assessment of patient with NMDs which requires a quantitative progress chart to monitor the therapeutic value of the treatment being administered. The proposed design of such a matrix is shown in the Figure 2. The approach to obtain this RAM is discussed in the subsequent section. The integration of the proposed RAM to existing PMR assessment reports will provide the therapist measurable objectives for monitoring the patient&rsquo;s progress during the course of assistive rehabilitation. A motor unit refers to an &alpha;-motor neuron of the Central Nervous System and the set of muscle fibres it innervates. When a motor unit (MU) is recruited, it contributes a quantum of force to muscular contraction [13]. The changes in the active MU density are attributable to age, buildup, disease and injury. It is observed that though MU density reduces with age, it is not as severe as the effects due to NMDs. It is observed to be a very useful parameter to monitor neurogenic disease progression, motor-neuron death rate and motor development improvements during rehabilitation [14]. The active MU density in Biceps Brachii muscle has been reported as average of 109 per mm2 (Std. Dev.: 53 per mm2 ) for a stroke related myopathy patient and about 153 per mm2 (Std. Dev.: 38 per mm2 ) for a normal subject [15]. The number of active motor units per unit area, inferred from the EMG has been recorded in the X-axis of the RAM. The axis has been sub-divided into 8 classes with a class width of 15 active MUs per mm2 (shown in Fig. 2). However, it must be noted that this work does not delve into Motor Unit Number Estimation (MUNE) methods. Researchers have developed enhanced statistical approaches for MUNE like Bayesian Estimators [16], Poisson Techniques [17], Higher Order Statistics [18] and SpatioTemporal Summation approaches [19]. Figure 2. Rehabilitation Assessment Matrix The Y+ -axis of the RAM (shown in Figure 2) refers to the myopathic affected fibre fraction representing the degree of myopathy whereas the Y-- -axis refers to the neuropathic motor unit Myopathy Progress Curve Neuropathy Progress Curve International Journal on Bioinformatics &amp; Biosciences (IJBB) Vol.3, No.3, September 2013 28 loss fraction corresponding to the degree of neuropathy. As treatment progresses, the subject&rsquo;s improvement line, both Myopathy Progress Curve and Neuropathy Progress Curve (Sample highlighted in Figure 2) moves towards the Normal body functioning line. The pattern followed in the RAM reflects the subject&rsquo;s motor learning ability and can provide useful insights into the nature of exercise the physiotherapist can administer to the subject. If the subject&rsquo;s curve is not progressive as desired, the physiotherapist&rsquo;s may be alerted to a need for change in the exercise routine and treatment being administered. 4. PHYSIOLOGICAL DATA ACQUISITION, PRE-PROCESSING AND FEATURE EXTRACTION The Electromyogram signals were synthetically generated using a physiological model developed by Wright and Stashuk. This model generates EMG signals consistent with those acquired through intramuscular needle electrodes from the limb muscles (including biceps brachii) of human subjects [20]. Though the Kinesiological EMG acquired through intramuscular electrodes is invasive over surface electrodes, it is preferred for neuromuscular disease prognosis due to its increased signal specificity and more selective recording to characterize the muscle of interest [21]. The EMG signal was generated at 31,250 Hz and band pass filtered from 10 to 10,000 Hz to remove enhance signal characteristics. The selected muscle and motorneuron pool settings of the Wright-Stashuk model correspond to the biceps brachii muscle of a human subject, simulating a constant force isometric contraction without fatigue or spasm. Isometric contractions are static muscle contractions which happen without any appreciable decrease in fibre length and change in the distance between point of electrode insertion and origin of EMG signals. The subject-age and gender were not fixed during each simulation to minimize any fixed-variable bias and enhance data set universality. The simulated intra-muscular needle electrode configuration, contraction type and the muscle model parameters are described in Table 1. Table 1. Description of parameters for EMG Generation S.N. Type of Parameter Description 1 Electrode Configuration Differential Electrode Configuration Detection Surfaces Dimension: Length: 1.0cm; Width: 1.2mm; Separation: 1.0 cm Bandwidth: 20-500Hz with a 40 dB/decade roll-off. Common Mode Rejection Ratio: &gt; 80dB Noise: &lt; 2&micro;V rms (20-400 Hz)Input Impedance: &gt; 100 M&Omega; 2 Electrode Location Middle line of Muscle Belly between the myotendonous junction and nearest innervation zone. 3 Muscle Model Parameters Contraction Level ( % MVC): 5-50% No. of Active MU Density: 75-180 per mm2 4 Disease Parameters Neuropathic Motor Unit Loss Fraction: 0.0(Healthy)-1.0 (Extreme) Step Size: 0.25 Myopathic Fiber Affected Fraction:0.0(Healthy)-1.0 (Extreme) Step Size: 0.25 4.1. Synthetic EMG Generation from Wright-Stashuk Model A total of 2000 sample-waveforms (10 Contraction-levels &times; 8 Classes of Active MU Density &times; 5 Classes of Myopathy &times; 5 Classes of Neuropathy) were synthetically generated for 5 seconds at a sample rate of 31,250 Hz. The objective behind introducing high degree of inter-simulation variability is to develop a universal approach that can be readily extended to medical domain. International Journal on Bioinformatics &amp; Biosciences (IJBB) Vol.3, No.3, September 2013 29 The algorithms and codes for analysis have been written in MATLAB R2010b&reg; and use the inbuilt Statistics, System Identification and Neural Network Toolboxes. 4.2. Physiological Feature Extraction In the present case, the generated signals were filtered for suppressing signal aliasing and motion artifacts using a 5th order Savitsky Golay Filter. The filter fits a 5th order polynomial in a window of 41 data points. It reduces noise while preserving the waveform&rsquo;s shape, structure, the relative maxima, minima and width [22]. The smoothened signal representing muscle force for the three real-life test signals has been shown in the Figure 3.The filtered muscle data is partitioned into static windows and the features extracted from each window will constitute the characteristic feature vector. The optimal window size for this particular application is expected to vary between 100ms and 1s. Therefore, classifier&rsquo;s decision making performance would be evaluated for good trade-off between accuracy and specificity, over 10 windows from 100ms to 1s in steps of 100ms. The extracted features are explained in the following subsections. Figure 3. Savitsky-Golay Filtering 4.2.1. Statistical Features These features help in assessment of uncertainty associated with physiological signal. De Luca et al. demonstrated that time-domain statistical features of EMG are influenced by MU firing rate, number of detected active MU, the MU activation potential, duration, waveform morphology and the recruitment stability [9]-[23]. The statistical features extracted include: Global Maxima, Global Minima, Mean, Standard Deviation, Energy, Time Duration, Bandwidth, Time Bandwidth Product, 3rd order moment, 4th order moment, 5th order moment, Root Mean Square Value, Kurtosis and Skewness as tabulated in Table 2. Table 2. Statistical Features of EMG Signal S.N. Feature Name Formula S.N. Feature Name Formula 1 Global Maxima Max(x[n]) 8 Time Bandwidth Product TD  BW International Journal on Bioinformatics &amp; Biosciences (IJBB) Vol.3, No.3, September 2013 30 2 Global Minima Min(x[n]) 9 3 rd Order Moment   N i x i N 1 3 [ ] 1 3 Mean    N i x i N x 1 [ ] 1  10 4 th Order Moment   N i x i N 1 4 [ ] 1 4 Std. Dev.     N i x i x N s 1 2 ( [ ] ) 1  11 5 th Order Moment   N i x i N 1 5 [ ] 1 5 Energy   N i x i 1 2 [ ] 12 Root Mean Square   N i x i N 1 2 [ ] 1 6 Time Duration 1/2 1 2 [ ] 1 2 [ ] 2 ( )                 N i x i N i i i x i TD  13 Kurtosis 4 ( 1) 1 4 ( [ ] ) N s N i x i x      7 Bandwidth 1/2 1 2 [] 2 2 ( [ ] [ 1]) 2 1                  N i x i N i x i x i BW  14 Skewness 3 ( 1) 1 3 ( [ ] ) N s N i x i x      4.2.2. Spectral Features In studies on rehabilitation, it is desirable to predict fatigue before it commences so that appropriate remedies may be adopted. Researchers have used the contractile force approach for evaluating fatigue points when the subject undergoes sustained contraction. Changes in the muscle force and the monitored torque indicate progress of fatigue with time. But, this method is considered inefficient as force and torque provide only a general overview of the entire muscle and not the individual motor units. In this context, the spectral modification during compression, along with the alteration of the skewness of the EMG waveform is acceptable as a Fatigue Index. EMG gives a more holistic view on muscle fatigue as individual skeletal muscle can be monitored continuously from the point of onset of the contraction. The Figure 4 below illustrates the factors of EMG which influence the spectral modification property and its interrelationships. Figure 4. Factors influencing spectral characteristics of EMG waveform Researchers have observed spectral modifications in the power spectrum of EMG acquired during tetanic muscular contractions (Tetanic refers to sustained muscle contraction without rest intervals). The skewness of the MUAP waveform is observed to alter with increasing fatigue and changes in muscle biochemistry due to continuous accumulation of lactic acid in the muscle cell (Anaerobic Respiration) [24]. The power spectrum of EMG signals was estimated using the Lomb periodogram approach because of its robustness to motion artifacts and missed data points International Journal on Bioinformatics &amp; Biosciences (IJBB) Vol.3, No.3, September 2013 31 and lesser computational complexity for real-life biomedical applications [25]. Let S (f) represent the Lomb periodogram of the EMG signal over an input range of f: 10Hz to 10000Hz (Frequency Resolution &Delta;f: 1 Hz). The spectral features extracted are the mean, median and the maximum frequency which are given by formulae (1)-(3) respectively. (1) ( ) ( ) 10000 10 10000 10           f f mean s f f f s f f f ( ) (2) 2 1 10000 10     f median f s f f arg max( ( )) (3) max f s f imum  f 4.2.3. Cepstral Features Cepstral Coefficients are calculated from the inverse Fourier Transform of the logarithmic power spectrum of EMG. Yoshikawa et al. established that the lower order Cepstral coefficients extracted from EMG can be used in robust classification of hand motions [26].These cepstral coefficients are derived from the 10th order autoregressive model of the filtered EMG signal. Let x(k) represent the filtered EMG signal, ai is the i th coefficient of the M-order autoregressive model and e(k) is the white noise in the system (refer Formula (4)). The cepstral coefficients ci (i=1:5) are derived from ai using recursive formulae (5)-(6). ( ) ( ) ( ) (4) 10 1       M i i x k a x k i e k ( 5 ) 1 1 c   a 1 1 1 1               n i i n i i a c i n c a where 1<em> 0.452 the subject is classified as Unhealthy. For such a cutoff, the sensitivity of classifier performance was observed as 91.35% and the overall specificity was 85.3%. International Journal on Bioinformatics &amp; Biosciences (IJBB) Vol.3, No.3, September 2013 36 Further, the designed classifier for the optimal window size of 400 ms is tested against the human Kinesiological EMG data acquired from Physionet signal database and the observed outputs from the network are tabulated in Table 5. The data includes intracellular EMG signals acquired from the biceps brachii muscle from three human subjects: a 44-year old man without any medical history of neuromuscular disease, a 62-year old man with chronic lower back pain and neuropathy and a 57-year old man with myopathy [10]. As observed from ROC analysis, the network&rsquo;s output cut-off of 0.452 is used to demarcate the healthy subject from an unhealthy subject. It is hence observed that the developed classifier accurately classifies the presented human subject acquired signals into their respective classes thus provides a proof-of-concept for the presented approach. Table 5. Results of Testing Real-Life EMG Data Against the Trained CCNN S.N. Class of Patient Target Data Avg. Output Network Output 1. H 0.0 0.1186 H 2. UH: M 1.0 0.7874 UH 3. UN: N 1.0 0.8755 UH Legend: H: Healthy UH: Unhealthy M: Myopathic N: Neuropathic For investigating the extendibility of CCNN Classifier technique to perform NMD diagnosis using dynamic isotonic contractions, the 22-attribute feature vector was extracted for a time window of 400ms from the data acquired using protocols described in Section 6. Since the subject is a healthy subject, the performance analysis metrics for testing the classifier here were decided as the output mean square error (MSE) as against accuracy and specificity. The observations are tabulated in Table 6. The data from Trail 01 and Trial 02 were diagnosed correctly and the misclassification of Healthy into Unhealthy for Trial 03 must be noted. Since the performance of Trial 02 data is better that Trail 01 and Trial 03, it is proposed that for extending the CCNN Classifier to dynamic isotonic contractions, the EMG data must be acquired through slow and steady flexion and extension motions. Table 6. Results of Testing CCNN Against Isotonic Contractions S.N. Trial Speed Target Data Avg. Output Diagnosis MSE Observed 1. T 01 Normal 1.0 0.7421 Healthy 3.211E-01 2. T 02 Slow 1.0 0.8745 Healthy 1.602E-01 3. T 03 Fast 1.0 0.4352 Unhealthy 6.458E-01 In Table 7, similar works for NMD detection available in literature are presented. Although direct comparison is not feasible, the proposed strategy compares well since it is trained using EMG data incorporating varied levels of disease severity both in neuropathy and myopathy and the learning technique for neural network training (Cascade Correlation) ensures design of an optimal classifier for the application. Table 7. Performance Evaluation of Present Technique vs. Existing Literature S.N. Author/Research Group Technique Classification Accuracy 1. Chistoudoulou et al. [34] Modular Neural Network 79.6% 2. Pattichis et al. [3] Feed-forward Network+ Self Organizing Maps 80% 3. H.B. Xie et al.[35] Support Vector Machine 82.4% 4. H.B. Xie et al.[36] Hybrid Neuro-Fuzzy Systems 88.58% 5. This Work Cascade Correlation Neural Network 91.2%(Training) 89.7%(Testing) International Journal on Bioinformatics &amp; Biosciences (IJBB) Vol.3, No.3, September 2013 37 8. CONCLUSIONS AND FUTURE WORK The proposed diagnostic system for NMD detection utilizes the Cascade Correlation Neural Network learning methodology. The optimal window size for diagnosis was inferred as 400ms and the classification using CCN Networks resulted in 91.2% accuracy, 85.3% specificity and 91.35% sensitivity for training data. For testing data, the diagnostic yield was 89.7% accuracy and an acceptable specificity of 78.5%. The proof-of-concept for extending the CCN classifier to real-life isometric contraction is established by testing on real-life kinesiological data. Investigations on data acquired using isotonic elbow flexion and extension contractions established that this method can be extended to dynamic studies. Further, integration of the proposed Rehabilitation Assessment Matrix with existing Physical Medicine and Rehabilitation practices will provide measurable objectives for therapists to monitor the patient&rsquo;s progress and help in preparing an appropriate medical treatment scheme to maximize the therapeutic value of the rehabilitation process. In the future, decision support systems to for NMD diagnosis will be developed which incorporate a multimodal diagnosis approach fusing EMG data with inferences from biochemical analysis, neuropathology and clinical observations. 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Lebiere (1990) &quot;The Cascade-Correlation Learning Architecture,&quot; Advances in Neural Information Processing Systems, Morgan-Kaufmann, Los Altos CA, 1990. [31] http://www.noraxon.com/products/instruments/myotrace400.php3 [32] G. Derringer and R. Suich, &quot;Simultaneous Optimization of Several Response Variables,&quot; Jour. of Qlty. Tech., vol. 12(4), pp. 214-219, 1980. [33] T. Fawcett, &ldquo;An Introduction to ROC Analysis,&rdquo; Pattern Recognition Letters, vol. 27, no. 8, pp. 861- 874, June 2006. [34] Christodoulou C.I., Pattichis C.S., 1995, &quot;A New Technique for the Classification and Decomposition of EMG signals&quot;, in Proc. IEEE Int. Conf. on Neural Networks, vol. 5, pp. 2303-2308, Nov. 1995. [35] H.B. Xie, Z. Wang , H. Huang, and C. Qing, &ldquo; SVM in Computer Aided Clinical EMG,&rdquo; 2nd Int. Conf. on M.L. and Cyb., pp. 1106-1108, 2003. [36] H.B. Xie, H. Huang, and Z. Wang, &ldquo; A Hybrid Neurofuzzy System for Neuromuscular Disorders Diagnosis,&rdquo; IEEE Workshop on Biomedical Circuits and Systems, Sec. 2.5, pp. 5-8, 2004. International Journal on Bioinformatics &amp; Biosciences (IJBB) Vol.3, No.3, September 2013 39 Authors Sailesh Conjeti holds a Bachelor of Engineering (Hons.) Degree in Electrical and Electronics Engineering from Birla Institute of Technology and Science, Pilani. He is currently with the School of Medical Science and Technology at Indian Institute of Technology, Kharagpur pursuing his Masters in Medic al Imaging and Informatics. His research interests include Medical Image Computing, Biomedical Signal Processing, Wearable Computing and Rehabilitation Engineering. He has participated in 5 research projects and has 8 publications to his credit. B. K. Rout completed his B. E. in Mechanical Engineering from University College of Engineering, Burla, Sambalpur (Deemed University) in the year 1990 and completed M. Tech, in Quality, Reliability and Operations Research from Indian Statistical Institute Calcutta, 1992. After graduation he worked with Escort Ancillaries and MESCO Steel Projects for 5 years. He joined BITS Pilani, in December 1998. For the last 12 years he is working as a Faculty member of Mechanical Engineering Group. While serving as a faculty member in the department of Mechanical Engineering, he completed his doctoral research in area of manipulator design under the guidance of Prof. R K Mittal in 2006. So far he has published many research papers in National and International Conferences and in International Journals. His areas of interests are Simulation and Optimization of Dynamic Systems, Design Optimization and Quality Engineering. </em>