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1

Isidori, Alberto. "Feedback control of nonlinear systems." International Journal of Robust and Nonlinear Control 2, no. 4 (1992): 291–311. http://dx.doi.org/10.1002/rnc.4590020404.

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2

Fradkov, Alexander L., Robin J. Evans, and Boris R. Andrievsky. "Control of chaos: methods and applications in mechanics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1846 (2006): 2279–307. http://dx.doi.org/10.1098/rsta.2006.1826.

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A survey of the field related to control of chaotic systems is presented. Several major branches of research that are discussed are feed-forward (‘non-feedback’) control (based on periodic excitation of the system), the ‘Ott–Grebogi–Yorke method’ (based on the linearization of the Poincaré map), the ‘Pyragas method’ (based on a time-delayed feedback), traditional for control-engineering methods including linear, nonlinear and adaptive control. Other areas of research such as control of distributed (spatio-temporal and delayed) systems, chaotic mixing are outlined. Applications to control of chaotic mechanical systems are discussed.
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3

MARUYAMA, Akira, Hiroyuki KAWAI, and Masayuki FUJITA. "Passivity-based Visual Feedback Control of Nonlinear Mechanical Systems." Transactions of the Institute of Systems, Control and Information Engineers 15, no. 12 (2002): 627–35. http://dx.doi.org/10.5687/iscie.15.627.

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4

Chang, Wook, Jin Bae Park, Young Hoon Joo, and Guanrong Chen. "Output Feedback Fuzzy Control for Uncertain Nonlinear Systems." Journal of Dynamic Systems, Measurement, and Control 125, no. 4 (2003): 521–30. http://dx.doi.org/10.1115/1.1636192.

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In this paper, a fuzzy control scheme, which employs the output feedback control approach, is suggested for the stabilization of nonlinear systems with uncertainties. The uncertain nonlinear system can be represented by uncertain Takagi-Sugeno (TS) fuzzy model structure, which is further rearranged to give a set of uncertain linear systems. A switching-type fuzzy-model-based controller, which utilizes the static output feedback control strategy, is designed based on this preliminary study. Theoretical analysis guarantees that under the control of the proposed technique, the uncertain nonlinear system is stabilizable by the switching-type static output-feedback fuzzy-model-based controller. Finally, two computer simulation examples are provided to show the effectiveness and feasibility of the developed controller design method.
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5

Tzou, H. S., D. D. Johnson, and K. J. Liu. "Damping Behavior Of Cantilevered Structronic Systems with Boundary Control." Journal of Vibration and Acoustics 121, no. 3 (1999): 402–7. http://dx.doi.org/10.1115/1.2893994.

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Distributed control of cantilever distributed systems using fully distributed piezoelectric layers has been investigated for years. The equivalent control actuation is introduced at the free end of the cantilever distributed systems, and the control action is equivalent to a counteracting control moment determined by the geometry, material properties, sensor signal, and control laws. In the negative proportional velocity feedback, the control effect is proportional to the feedback voltage and the controlled damping ratio usually exhibits linear behavior, if the feedback voltage is low. In this study, nonlinear damping behavior and an (equivalent) boundary changes of cantilever beams and plates with full-range feedback voltages are studied. Analytical solutions are compared with finite element simulations and experimental data. Studies suggest that the controlled damping ratio increases at low control gains and it decreases at high control gains induced by the boundary control moment. Furthermore, due to the highly constrained boundary control moment at high gains, the original fixed-free boundary condition can be approximated by an equivalent fixed/sliding-roller boundary condition.
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6

KIM, Dong Hun, Hua WANG, and Eung-Seok KIM. "Cascade Observers for Nonlinear Systems and Application to Nonlinear Output Feedback Control." JSME International Journal Series C 49, no. 2 (2006): 463–72. http://dx.doi.org/10.1299/jsmec.49.463.

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7

Elbeyli, O., and J. Q. Sun. "Covariance Control of Nonlinear Dynamic Systems via Exact Stationary Probability Density Function." Journal of Vibration and Acoustics 126, no. 1 (2004): 71–76. http://dx.doi.org/10.1115/1.1640355.

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This paper presents a method for designing covariance type controls of nonlinear stochastic systems. The method consists of two steps. The first step is to find a class of nonlinear feedback controls with undetermined gains such that the exact stationary PDF of the response is obtainable. The second step is to select the control gains in the context of the covariance control method by minimizing a performance index. The exact PDF makes the solution process of optimization very efficient, and the evaluation of expectations of nonlinear functions of the response very accurate. The theoretical results of various orders of response moments by the present method have been compared with Monte Carlo simulations. Special cases are studied when the approximate methods based on the maximum entropy principle or other closure schemes leads less accurate response estimates, while the present method still works fine.
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8

Hu, Xiaoming. "Stabilization of planar nonlinear systems by polynomial feedback control." Systems & Control Letters 22, no. 3 (1994): 177–85. http://dx.doi.org/10.1016/0167-6911(94)90011-6.

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9

Prach, Anna, Ozan Tekinalp, and Dennis S. Bernstein. "Output-feedback control of linear time-varying and nonlinear systems using the forward propagating Riccati equation." Journal of Vibration and Control 24, no. 7 (2016): 1239–63. http://dx.doi.org/10.1177/1077546316655913.

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For output-feedback control of linear time-varying (LTV) and nonlinear systems, this paper focuses on control based on the forward propagating Riccati equation (FPRE). FPRE control uses dual difference (or differential) Riccati equations that are solved forward in time. Unlike the standard regulator Riccati equation, which propagates backward in time, forward propagation facilitates output-feedback control of both LTV and nonlinear systems expressed in terms of a state-dependent coefficient (SDC). To investigate the strengths and weaknesses of this approach, this paper considers several nonlinear systems under full-state-feedback and output-feedback control. The internal model principle is used to follow and reject step, ramp, and harmonic commands and disturbances. The Mathieu equation, Van der Pol oscillator, rotational-translational actuator, and ball and beam are considered. All examples are considered in discrete time in order to remove the effect of integration accuracy. The performance of FPRE is investigated numerically by considering the effect of state and control weightings, the initial conditions of the difference Riccati equations, the domain of attraction, and the choice of SDC.
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10

Boothby, William M., and Riccardo Marino. "Feedback stabilization of planar nonlinear systems." Systems & Control Letters 12, no. 1 (1989): 87–92. http://dx.doi.org/10.1016/0167-6911(89)90100-x.

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11

Bennett, W. H., C. LaVigna, H. G. Kwatny, and G. Blankenship. "Nonlinear and Adaptive Control of Flexible Space Structures." Journal of Dynamic Systems, Measurement, and Control 115, no. 1 (1993): 86–94. http://dx.doi.org/10.1115/1.2897412.

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This paper addresses design of nonlinear control systems for rapid, large angle multiaxis, slewing and LOS pointing of realistic flexible space structures. The application of methods based on adaptive feedback linearization for nonlinear control design for flexible space structures is presented. A comprehensive approach to modeling the nonlinear dynamics and attitude control of multibody systems with structural flexure is considered. Adaptive feedback linearizing control laws are described based on Lagrangian dynamical system model for the spacecraft. Simulation results for attitude slewing and LOS stabilization for the NASA/IEEE Spacecraft COntrols Laboratory Experiment (SCOLE) design challenge are presented.
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12

Isidori, Alberto. "H∞ control via measurement feedback for affine nonlinear systems." International Journal of Robust and Nonlinear Control 4, no. 4 (1994): 553–74. http://dx.doi.org/10.1002/rnc.4590040409.

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13

Montano, O. E., Y. Orlov та Y. Aoustin. "Nonlinear state feedback ℋ ∞ -control of mechanical systems under unilateral constraints". IFAC Proceedings Volumes 47, № 3 (2014): 3833–38. http://dx.doi.org/10.3182/20140824-6-za-1003.00299.

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14

Montano, O. E., Y. Orlov, and Y. Aoustin. "Nonlinear output feedback H∞-control of mechanical systems under unilateral constraints." IFAC-PapersOnLine 48, no. 11 (2015): 274–79. http://dx.doi.org/10.1016/j.ifacol.2015.09.197.

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15

Mobayen, Saleh, and Fairouz Tchier. "Composite nonlinear feedback control technique for master/slave synchronization of nonlinear systems." Nonlinear Dynamics 87, no. 3 (2016): 1731–47. http://dx.doi.org/10.1007/s11071-016-3148-8.

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16

Engel, Robert, and Gerhard Kreisselmeier. "Nonlinear approximate observers for feedback control." Systems & Control Letters 56, no. 3 (2007): 230–35. http://dx.doi.org/10.1016/j.sysconle.2006.10.003.

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17

Kovaleva, A. "Control of autoresonance in mechanical and physical models." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2088 (2017): 20160213. http://dx.doi.org/10.1098/rsta.2016.0213.

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Autoresonant energy transfer has been considered as one of the most effective methods of excitation and control of high-energy oscillations for a broad range of physical and engineering systems. Nonlinear time-invariant feedback control provides effective self-tuning and self-adaptation mechanisms targeted at preserving resonance oscillations under variations of the system parameters but its implementation may become extremely complicated. A large class of systems can avoid nonlinear feedback, still producing the required state due to time-variant feed-forward frequency control. This type of control in oscillator arrays employs an intrinsic property of a nonlinear oscillator to vary both its amplitude and the frequency when the driving frequency changes. This paper presents a survey of recently published and new results studying possibilities and limitations of time-variant frequency control in nonlinear oscillator arrays. This article is part of the themed issue ‘Horizons of cybernetical physics’.
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18

Sira-Ramı´rez, Hebertt, and Orestes Llanes-Santiago. "Sliding Mode Control of Nonlinear Mechanical Vibrations1." Journal of Dynamic Systems, Measurement, and Control 122, no. 4 (2000): 674–78. http://dx.doi.org/10.1115/1.1316788.

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In this article we illustrate how the property of differential flatness can be advantageously joined to the sliding mode controller design methodology for the active stabilization of nonlinear mechanical vibration systems. The proposed scheme suitably combines off-line trajectory planning and an on-line “smoothed” sliding mode feedback trajectory tracking scheme for regulating the evolution of the flat output variables toward the desired equilibria. [S0022-0434(00)00404-4]
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19

Long, T. W., and C. K. Carrington. "The RAPT Control Method for Nonlinear Systems." Journal of Dynamic Systems, Measurement, and Control 113, no. 4 (1991): 736–41. http://dx.doi.org/10.1115/1.2896483.

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The Rapid Advancement Preview Tracking (RAPT) control method uses both a nonlinear system model and a linearized system model to provide a form of feedback/preview control for nonlinear systems. It uses measurements of the states to calculate the current preview control signal from a local linearization of the state equations, and then iteratively calculates a perturbation correction for that control using the nonlinear equations. The corrected control signal is then applied to the system, driving the end-effector to the next position along a specified trajectory. Computer simulations of tracking control for two-link planar manipulators indicate that this algorithm may be fast enough for real-time control.
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20

Li, Yan, and Yuanchun Li. "A unified framework of rapid exponential stability and optimal feedback control for nonlinear systems." Advances in Mechanical Engineering 11, no. 3 (2019): 168781401983320. http://dx.doi.org/10.1177/1687814019833206.

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A novel framework of rapid exponential stability and optimal feedback control is investigated and analyzed for a class of nonlinear systems through a variant of continuous Lyapunov functions and Hamilton–Jacobi–Bellman equation. Rapid exponential stability means that the trajectories of nonlinear systems converge to equilibrium states in accelerated time. The sufficient conditions of rapid exponential stability are developed using continuous Lyapunov functions for nonlinear systems. Furthermore, according to a variant of continuous Lyapunov functions, a rapid exponential stability is guaranteed which satisfies some canonical conditions and Hamilton–Jacobi–Bellman equation for controlled nonlinear systems. It is can be seen that the solution of Hamilton–Jacobi–Bellman equation is a continuous Lyapunov function, and, therefore, rapid exponential stability and optimality are guaranteed for nonlinear systems. Last, the main result of this article is investigated via a nonlinear model of a spacecraft with one axis of symmetry through simulations and is used to check rapid exponential stability. Moreover, for the disturbance problem of initial point, a rapid exponential stable controller can reject the large-scale disturbances for controlled nonlinear systems. In addition, the proposed optimal feedback controller is applied to the tracking trajectories of 2-degree-of-freedom manipulator, and the numerical results have illustrated high efficiency and robustness in real time. The simulation results demonstrate the use of the rapid exponential stability and optimal feedback approach for real-time nonlinear systems.
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21

Mamakoukas, Giorgos, Malcolm A. MacIver, and Todd D. Murphey. "Feedback synthesis for underactuated systems using sequential second-order needle variations." International Journal of Robotics Research 37, no. 13-14 (2018): 1826–53. http://dx.doi.org/10.1177/0278364918776083.

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This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions, the second-order needle variations of optimal control, as the basis for choosing each control response to the current state. A second result of this paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Finally, the underactuated dynamic underwater vehicle model demonstrates convergence even in the presence of a velocity field.
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22

Liu, Yan-Jun, and Yuan-Xin Li. "Adaptive fuzzy output-feedback control of uncertain SISO nonlinear systems." Nonlinear Dynamics 61, no. 4 (2010): 749–61. http://dx.doi.org/10.1007/s11071-010-9684-8.

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23

Wen, Guo-Xing, Yan-Jun Liu, Shao-Cheng Tong, and Xiao-Li Li. "Adaptive neural output feedback control of nonlinear discrete-time systems." Nonlinear Dynamics 65, no. 1-2 (2010): 65–75. http://dx.doi.org/10.1007/s11071-010-9874-4.

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24

Cao, D. Q., Y. M. Ge, and Y. R. Yang. "Stability Criteria for Nonclassically Damped Systems With Nonlinear Uncertainties." Journal of Applied Mechanics 71, no. 5 (2004): 632–36. http://dx.doi.org/10.1115/1.1778719.

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The asymptotic stability of nonclassically damped systems with nonlinear uncertainties is addressed using the Lyapunov approach. Bounds on nonlinear perturbations that maintain the stability of an asymptotically stable, linear multi-degree-of-freedom system with nonclassical damping are derived. The explicit nature of the construction permits us to directly express the algebraic criteria in terms of plant parameters. The results are then applied to the symmetric output feedback control of multi-degree-of-freedom systems with nonlinear uncertainties. Numerical examples are given to demonstrate the new stability criteria and to compare them with the previous results in the literature.
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25

Malas, Anindya, and Shyamal Chatterjee. "Modal self-excitation in a class of mechanical systems by nonlinear displacement feedback." Journal of Vibration and Control 24, no. 4 (2016): 784–96. http://dx.doi.org/10.1177/1077546316651786.

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Many devices and processes utilize self-excited oscillation to enhance performance. Recently, much research work has been devoted to the induction of self-excited oscillation in mechanical systems by nonlinear feedback. The present paper investigates the efficacy of a displacement feedback technique in generating self-excited oscillation at the desired mode(s) in a multiple degrees-of-freedom mechanical system. The controller couples the system with a bank of second-order filters and generates the required control force as a nonlinear function of the filter output. The describing function method theoretically explores the dynamics of the system with the control law. The control cost of the controller is studied for the proper choice of the filter parameters. The analytical results are substantiated by the numerical simulation results. The present study reveals that the proposed control laws, if used in an appropriate way, can generate self-excited oscillation in the system at the desired mode(s).
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26

Marino, Riccardo. "Feedback stabilization of single-input nonlinear systems." Systems & Control Letters 10, no. 3 (1988): 201–6. http://dx.doi.org/10.1016/0167-6911(88)90053-9.

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27

Ball, Joseph A., and Madan Verma. "Factorization and feedback stabilization for nonlinear systems." Systems & Control Letters 23, no. 3 (1994): 187–96. http://dx.doi.org/10.1016/0167-6911(94)90004-3.

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28

Liu, Xinxin, Xiaojie Su, and Peng Shi. "Event‐triggered dynamic output feedback control for networked nonlinear systems." International Journal of Robust and Nonlinear Control 30, no. 17 (2020): 7031–51. http://dx.doi.org/10.1002/rnc.5161.

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29

Bowong, S., F. M. Moukam Kakmeni, and C. Tchawoua. "Chaos Control and Synchronization of a Class of Uncertain Chaotic Systems." Journal of Vibration and Control 11, no. 8 (2005): 1007–24. http://dx.doi.org/10.1177/1077546305052040.

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This paper deals with the control and synchronization of chaotic systems. First, a control strategy is developed to control a class of uncertain nonlinear systems. The proposed strategy is an input-output control scheme, which comprises an uncertainty estimator and an exponential linearizing feedback. Computer simulations are provided to illustrate the operation of the designed synchronization scheme.
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30

Shergei, M., and U. Shaked. "RobustH∞ nonlinear control via measurement feedback." International Journal of Robust and Nonlinear Control 7, no. 11 (1997): 975–87. http://dx.doi.org/10.1002/(sici)1099-1239(199711)7:11<975::aid-rnc245>3.0.co;2-4.

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31

Shamma, Jeff S. "Nonlinear state feedback for ℓ1 optimal control". Systems & Control Letters 21, № 4 (1993): 265–70. http://dx.doi.org/10.1016/0167-6911(93)90067-g.

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32

Anderson, M. J., and W. J. Grantham. "Lyapunov Optimal Feedback Control of a Nonlinear Inverted Pendulum." Journal of Dynamic Systems, Measurement, and Control 111, no. 4 (1989): 554–58. http://dx.doi.org/10.1115/1.3153091.

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Lyapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which “rocks” the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Lyapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.
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33

Narikiyo, T., and T. Izumi. "On Model Feedback Control for Robot Manipulators." Journal of Dynamic Systems, Measurement, and Control 113, no. 3 (1991): 371–78. http://dx.doi.org/10.1115/1.2896420.

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Robot manipulators are highly coupled nonlinear systems and their motions are influenced by uncertain dynamics such as coulomb friction. These nonlinearities and uncertainties disturb the performance of control systems. In this paper, a control design methodolgy is proposed for the purpose of reducing the adverse effects of parameter uncertainties and disturbances. This control structure is similar to that of classical control. Unlike classical control, this control methodology accommodates multivariate control systems with uncertain dynamics and disturbances. The control design methodology is applied to a three-degrees-of-freedom directly driven robot. Simulation and experimental results demonstrate excellent robustness.
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34

António Tenreiro Machado, José, and Behrouz Parsa Moghaddam. "A Robust Algorithm for Nonlinear Variable-Order Fractional Control Systems with Delay." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 3-4 (2018): 231–38. http://dx.doi.org/10.1515/ijnsns-2016-0094.

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AbstractIn this paper, we propose a high-accuracy linear B-spline finite-difference approximation for variable-order (VO) derivative. We consider VO fractional differentiation as a control parameter for improving the stability in systems exhibiting vibrations. The method is applied to nonlinear feedback with VO fractional derivative. The results demonstrate the efficiency and high accuracy of the novel algorithm.
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35

Zhang, Fukai, and Cong Wang. "Deterministic learning from neural control for uncertain nonlinear pure‐feedback systems by output feedback." International Journal of Robust and Nonlinear Control 30, no. 7 (2020): 2701–18. http://dx.doi.org/10.1002/rnc.4902.

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36

Liu, Xiao-Xiao, and Xing-Min Ren. "An IPEM for optimal control of uncertain beam-moving mass systems with saturation nonlinearity." Journal of Vibration and Control 24, no. 13 (2017): 2760–81. http://dx.doi.org/10.1177/1077546317693957.

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This paper addresses the vibration control of single-span beams subjected to a moving mass by coupling the saturated nonlinear control and an improved point estimation method (IPEM). An optimal nonlinear feedback control law, for a kind of uncertain linear system with actuator nonlinearities, is derived using the combination of Pontryagin's maximum principles and the improved point estimation method. The stability of the feedback system is guaranteed using a Lyapunov function. In order to obtain the instantaneously probabilistic information of output responses, a novel moment approach is presented by combining the improved point estimation method, the maximum entropy methodology and the probability density evolution theory. In addition to the consideration of stochastic system parameters, the external loadings are considered as a nonstationary random excitation and a moving sprung mass, respectively. The proposed strategy is then used to perform vibration suppression analysis and parametric sensitivity analysis of the given beam. From numerical simulation results, it is deduced that the improved point estimation method is a priority approach to the optimal saturated nonlinear control of stochastic beam systems. This observation has widespread applications and prospects in vehicle–bridge interaction and missile–gun systems.
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37

Z˙ak, S. H. "An Eclectic Approach to the State Feedback Control of Nonlinear Dynamical Systems." Journal of Dynamic Systems, Measurement, and Control 111, no. 4 (1989): 631–40. http://dx.doi.org/10.1115/1.3153106.

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This paper examines the problem of robust state-feedback stabilization of a class of nonlinear multi-input dynamical systems. Four approaches to the problem are investigated: the variable structure control (VSC) method, the high-gain feedback technique, the feedback linearization algorithm, and finally the deterministic approach to the control of uncertain systems. It is shown that each design method can lead to a controller such that the closed-loop system exhibits a sliding mode property. The sliding mode is a desirable property since it results in a robust control. The analysis is illustrated by means of a simple numerical example.
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38

Gogoussis, Aristides, and Max Donath. "Reciprocal Variable Feedback: Induced Sensing for Nonlinear Systems Design and Control." Journal of Dynamic Systems, Measurement, and Control 120, no. 2 (1998): 157–63. http://dx.doi.org/10.1115/1.2802404.

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System performance can be significantly improved when both the design of the plant and of the controller are considered concurrently. Control theory can be applied to a broad variety of systems, including those that are physical in nature and many that are not. Despite the generality of control theory, there are many situations in which opportunities are missed for using less conservative control laws and simpler overall implementations. This is due to the use of formulations that do not explicitly reveal the existence of intrinsic information pertaining to the particular domain of application. Such is the case with many physical systems. However, the various constraints associated with physical reality (in the form of principles, laws, etc.) open up several possibilities which can be exploited for system design and control. In this paper, we propose the Reciprocal Variable Feedback principle as a means for facilitating the control of plants with complicated nonlinear dynamics in the presence of parameter and/or structural uncertainty. The RVF principle exploits the effort-flow relationships associated with power interactions in order to assist in the design and control of physical processes. This is accomplished by using appropriate sensors instead of computation based on models (e.g., feedback linearization) and can be implemented within many physical domains. A motion control example is used to provide insight into the nature of the principle. It is expected that in the future, additional principles will be identified and introduced for integrating design with the control of dynamical systems.
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39

Annaswamy, A. M., and D. Seto. "Object Manipulation Using Compliant Fingerpads: Modeling and Control." Journal of Dynamic Systems, Measurement, and Control 115, no. 4 (1993): 638–48. http://dx.doi.org/10.1115/1.2899191.

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Current industrial robots are often required to perform tasks requiring mechanical interactions with their environment. For tasks that require grasping and manipulation of unknown objects, it is crucial for the robot end-effector to be compliant to increase grasp stability and manipulability. The dynamic interactions that occur between such compliant end-effectors and deformable objects that are being manipulated can be described by a class of nonlinear systems. In this paper, we determine algorithms for grasping and manipulation of these objects by using adaptive feedback techniques. Methods for control and adaptive control of the underlying nonlinear system are described. It is shown that although standard geometric techniques for exact feedback linearization techniques are inadequate, yet globally stable adaptive control algorithms can be determined by making use of the stability characteristics of the underlying nonlinear dynamics.
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40

El-Farra, Nael H., Prashant Mhaskar, and Panagiotis D. Christofides. "Output feedback control of switched nonlinear systems using multiple Lyapunov functions." Systems & Control Letters 54, no. 12 (2005): 1163–82. http://dx.doi.org/10.1016/j.sysconle.2005.04.005.

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41

Muñoz de la Peña, David, and Panagiotis D. Christofides. "Output feedback control of nonlinear systems subject to sensor data losses." Systems & Control Letters 57, no. 8 (2008): 631–42. http://dx.doi.org/10.1016/j.sysconle.2008.01.005.

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42

Byrnes, Christopher I. "Remarks on nonlinear planar control systems which are linearizable by feedback." Systems & Control Letters 5, no. 6 (1985): 363–67. http://dx.doi.org/10.1016/0167-6911(85)90059-3.

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43

Fung, Rong-Fong, Jinn-Wen Wu, and Sheng-Luong Wu. "Stabilization of an Axially Moving String by Nonlinear Boundary Feedback." Journal of Dynamic Systems, Measurement, and Control 121, no. 1 (1999): 117–21. http://dx.doi.org/10.1115/1.2802428.

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In this paper, we consider the system modeled by an axially moving string and a mass-damper-spring (MDS) controller, applied at the right-hand side (RHS) boundary of the string. We are concerned with the nonlinear string and the effect of the control mechanism. We stabilize the system through a proposed boundary velocity feedback control law. Linear and nonlinear control laws through this controller are proposed. In this paper, we find that a linear boundary feedback caused the total mechanical energy of the system to decay an asymptotically, but it fails for an exponential decay. However, a nonlinear boundary feedback controller can stabilize the system exponentially. The asymptotic and exponential stability are verified.
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44

Butcher, E. A., and R. Lu. "Constant-Gain Linear Feedback Control of Piecewise Linear Structural Systems via Nonlinear Normal Modes." Journal of Vibration and Control 10, no. 10 (2004): 1535–58. http://dx.doi.org/10.1177/1077546304042065.

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We present a technique for using constant-gain linear position feedback control to implement eigen-structure assignment of n-degrees-of-freedom conservative structural systems with piecewise linear nonlinearities. We employ three distinct control strategies which utilize methods for approximating the nonlinear normal mode (NNM) frequencies and mode shapes. First, the piecewise modal method (PMM) for approximating NNM frequencies is used to determine n constant actuator gains for eigenvalue (pole) placement. Secondly, eigenvalue placement is accomplished by finding an approximate single-degree-of-freedom reduced model with one actuator gain for the mode to be controlled. The third strategy allows the frequencies and mode shapes (eigenstructure) to be placed by using a full n × n matrix of actuator gains and employing the local equivalent linear stiffness method (LELSM) for approximating NNM frequencies and mode shapes. The techniques are applied to a two-degrees-of-freedom system with two distinct types of nonlinearities: a bilinear clearance nonlinearity and a symmetric deadzone nonlinearity.
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45

Zhang, Minzhi, and R. M. Hirschorn. "Feedback stabilization of nonlinear systems by locally bounded controls." Systems & Control Letters 23, no. 4 (1994): 255–62. http://dx.doi.org/10.1016/0167-6911(94)90047-7.

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46

McClamroch, N. H. "Displacement Control of Flexible Structures Using Electrohydraulic Servo-Actuators." Journal of Dynamic Systems, Measurement, and Control 107, no. 1 (1985): 34–39. http://dx.doi.org/10.1115/1.3140704.

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A general approach to the displacement or position control of a nonlinear flexible structure using electrohydraulic servo actuators is developed. Our approach makes use of linear feedback of measured structural displacements plus linear feedback of the actuator control forces; a nonlinear feedforward function of the displacement command is also used for control. Based on a mathematical model of the closed loop, general conditions for closed loop stability are obtained. In the special case that the feedback is decentralized the stabilization conditions are stated in terms of simple inequalities; moreover, the stabilization conditions are robust to structural uncertainties since the conditions do not depend on explicit properties of the structure. Such robustness is a direct consequence of use of force feedback rather than, for example, acceleration feedback. Conditions are also developed for selection of the feedforward control to achieve zero steady state error; but this condition does depend on explicit properties of the structure. The theoretical results developed in the paper should provide a framework for advanced applications of control of mechanical systems using electrohydraulic servo-actuators.
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47

Zhou, Di, Tielong Shen, and Katsutoshi Tamura. "Adaptive Nonlinear Synchronization Control of Twin-Gyro Precession." Journal of Dynamic Systems, Measurement, and Control 128, no. 3 (2005): 592–99. http://dx.doi.org/10.1115/1.2232683.

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The slewing motion of a truss arm driven by a V-gimbaled control-moment gyro is studied. The V-gimbaled control-moment gyro consists of a pair of gyros that must precess synchronously. For open-loop slewing motion control, the controller design problem is simplified into finding a feedback controller to steer the two gyros to synchronously track a specific command. To improve the synchronization performance, the integral of synchronization error is introduced into the design as an additional state variable. Based on the second method of Lyapunov, an adaptive nonlinear feedback controller is designed. For more accurate but complicated closed-loop slewing motion control, the feedback linearization technique is utilized to partially linearize the nonlinear nominal model, where two specific output functions are chosen to satisfy the system tracking and synchronization requirements. The system tracking dynamics are bounded by properly determining system indices and command signals. For the partially linearized system, the backstepping tuning function design approach is employed to design an adaptive nonlinear controller. The dynamic order of the adaptive controller is reduced to its minimum. The performance of the proposed controllers is verified by simulation.
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48

Hua, Changchun, Xinping Guan, and Peng Shi. "Robust Decentralized Adaptive Control for Interconnected Systems With Time Delays." Journal of Dynamic Systems, Measurement, and Control 127, no. 4 (2005): 656–62. http://dx.doi.org/10.1115/1.2101845.

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The problem of robust stabilization for a class of time-varying nonlinear large-scale systems subject to multiple time-varying delays in the interconnections is considered. The interconnections satisfy the match condition, and are bounded by nonlinear functions that may contain a high-order polynomial with a time delay. Without the knowledge of these bounds, we present adaptive state feedback controllers that are continuous and independent of time delays. Based on the Lyapunov stability theorem, we prove that the controllers can render the closed loop systems uniformly ultimately bounded stable. We also apply the result to constructing adaptive feedback controllers to stabilize a class of interconnected systems whose nominal systems are linear. Finally, several examples are given to show the potential of the proposed techniques.
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49

Dayawansa, W., W. M. Boothby, and D. L. Elliott. "Global state and feedback equivalence of nonlinear systems." Systems & Control Letters 6, no. 4 (1985): 229–34. http://dx.doi.org/10.1016/0167-6911(85)90072-6.

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50

Lee, Kyun K., and Aristotle Arapostathis. "Remarks on smooth feedback stabilization of nonlinear systems." Systems & Control Letters 10, no. 1 (1988): 41–44. http://dx.doi.org/10.1016/0167-6911(88)90038-2.

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