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Journal articles on the topic 'The nonlinear control laws'

Author: Grafiati

Published: 4 June 2025

Last updated: 15 July 2025

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1

Liaw, Der-Cherng, Yew-Wen Liang, and Chiz-Chung Cheng. "Nonlinear Control for Missile Terminal Guidance." Journal of Dynamic Systems, Measurement, and Control 122, no. 4 (2000): 663–68. http://dx.doi.org/10.1115/1.1316796.

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Variable Structure Control (VSC) technique is applied to the design of robust homing missile guidance laws. In the design procedure, the target’s maneuver is assumed to be unpredictable and is considered as disturbances. Guidance laws are then proposed to achieve the interception performance for both cases of longitude-axis control being available and unavailable. The proposed guidance laws are continuous which alleviate chattering drawback by classic VSC design. Results are obtained and compared with those by realistic true proportional navigation design to illustrate the benefits of the proposed design. [S0022-0434(00)00604-3]

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2

Lu, P. "Optimal feedback control laws using nonlinear programming." Journal of Optimization Theory and Applications 71, no. 3 (1991): 599–611. http://dx.doi.org/10.1007/bf00941406.

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3

Freeman, R. A., and P. V. Kokotovic. "Design of ‘softer’ robust nonlinear control laws." Automatica 29, no. 6 (1993): 1425–37. http://dx.doi.org/10.1016/0005-1098(93)90007-g.

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4

Răsvan, Vladimir. "Control of Conservation Laws – An Application." Tatra Mountains Mathematical Publications 71, no. 1 (2018): 155–74. http://dx.doi.org/10.2478/tmmp-2018-0014.

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Abstract We present here three types of controlled boundary value problems for conservation laws arising from energy co-generation, hydraulic flows and water hammer for hydroelectric power plants and control of the open channel flows (shallow water). The novelty of these models, from the mathematical point of view, is that they are described by nonlinear hyperbolic partial differential equations of the conservation laws with (possibly) nonlinear boundary conditions. At their turn these boundary conditions are controlled by some systems of ordinary differential equations. The engineering requirements for such systems are asymptotic stability and disturbance rejection: these properties have to be achieved by feedback control. In our setting the main tool for tackling these problems is a suitable Lyapunov functional arising from the energy identity. The hints for “guessing” this functional are to be found in the linearized version of the aforementioned mathematical objects.

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5

El-Farra, Nael H., and Panagiotis D. Christofides. "Robust inverse optimal control laws for nonlinear systems." International Journal of Robust and Nonlinear Control 13, no. 15 (2003): 1371–88. http://dx.doi.org/10.1002/rnc.860.

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6

Mönnigmann, Martin, Jonas Otten, and Michael Jost. "Nonlinear MPC defines implicit regional optimal control laws." IFAC-PapersOnLine 48, no. 23 (2015): 142–47. http://dx.doi.org/10.1016/j.ifacol.2015.11.274.

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7

Tornambe`, A. "Control Laws Based on Parameter Observation." Journal of Dynamic Systems, Measurement, and Control 114, no. 2 (1992): 186–95. http://dx.doi.org/10.1115/1.2896514.

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This paper deals with the use of asymptotic observers in the parameter estimation. Exact and approximate procedures are proposed taking into account the nonlinear behaviour of the dynamic systems considered. It is shown that a separation property holds for sufficiently fast observers and, therefore, that parameter estimates obtained by asymptotic observers are useful for the implementation of feedback control laws. The paper is completed with an application to flexible robot arms for the estimation of the elastic constant. Simulation tests are included.

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8

Hu, Haiyun, Se Young Yoon, and Zongli Lin. "Consensus of Multi-Agent Systems with Control-Affine Nonlinear Dynamics." Unmanned Systems 04, no. 01 (2016): 61–73. http://dx.doi.org/10.1142/s2301385016400070.

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This paper studies the consensus problem for a class of multi-agent systems, where each agent is a nonlinear system affine in control. Distributed control laws are proposed for multi-agent systems with and without communication delays, respectively. It is shown that under undirected and connected communication network our control laws ensure the state consensus of multi-agent systems in both cases. The effectiveness of the proposed control laws is demonstrated by numerical simulation.

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9

Almashaal, Mohammad J., and Anatoly R. Gaiduk. "On the choice of the sample period of nonlinear hybrid control systems." Analysis and data processing systems, no. 1 (March 26, 2024): 7–20. http://dx.doi.org/10.17212/2782-2001-2024-1-7-20.

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Hybrid systems are often used in various technical applications, such as robotics, aviation, space, energy, etc. The emergence of hybrid control systems is due to the use of computers to implement control laws, including nonlinear ones. Digital means cannot implement continuous control laws. However, the known methods of design, especially of nonlinear systems, lead precisely to continuous controls, which caused the need to discretize the continuous control with the largest possible period. Solving the problem of determining the maximum permissible sampling period of a nonlinear control system is a rather complex stage of its creation. In this article the problem of definition of the maximum allowed sample period of the nonlinear hybrid system control and its dependence on the module of the maximum eigenvalue of the functional matrix of quasilinear model of the continuous system is also considered. The nonlinear hybrid system is created by discretizing the control of the nonlinear continuous system. This continuous system is synthesized using the algebraic polynomial and matrix method of the nonlinear control systems design in which quasilinear models are used. It has been is established that the value of the maximum permissible sample period depends not only on the module of the maximum eigenvalue, but also on initial conditions and external influences. These dependences are complex and it is difficult to find them theoretically. Experimentally, based on the example of the specific nonlinear hybrid control system it is shown that eigenvalues smaller on the module lead to larger values of the maximum of the permissible sample period. The problem of choosing the sample period of control laws of the real hybrid control systems can be solved in the similar way based on a compromise between the system high-speed performance and the sample period.

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10

Steinberg, Marc L. "Comparison of Intelligent, Adaptive, and Nonlinear Flight Control Laws." Journal of Guidance, Control, and Dynamics 24, no. 4 (2001): 693–99. http://dx.doi.org/10.2514/2.4796.

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11

Huang, Jie, and Ching-Fang Lin. "Numerical approach to computing nonlinear H-infinity control laws." Journal of Guidance, Control, and Dynamics 18, no. 5 (1995): 989–94. http://dx.doi.org/10.2514/3.21495.

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12

Walker, Daniel J., Mark Voskuijl, Binoy J. Manimala, and Arthur W. Gubbels. "Nonlinear Attitude Control Laws for the Bell 412 Helicopter." Journal of Guidance, Control, and Dynamics 31, no. 1 (2008): 44–52. http://dx.doi.org/10.2514/1.28945.

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13

Lu, Ping. "Approximate nonlinear receding-horizon control laws in closed form." International Journal of Control 71, no. 1 (1998): 19–34. http://dx.doi.org/10.1080/002071798221902.

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14

Rösch, Arnd. "Identification of nonlinear heat transfer laws by optimal control." Numerical Functional Analysis and Optimization 15, no. 3-4 (1994): 417–34. http://dx.doi.org/10.1080/01630569408816573.

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15

Teppa, Pedro, Jacques Bernussou, and Germain García. "Scheduling of Local Robust Control Laws for Nonlinear Systems." IFAC Proceedings Volumes 37, no. 21 (2004): 645–50. http://dx.doi.org/10.1016/s1474-6670(17)30543-8.

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16

Xia, X. "Parameterization of decoupling control laws for affine nonlinear systems." IEEE Transactions on Automatic Control 38, no. 6 (1993): 916–28. http://dx.doi.org/10.1109/9.222303.

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17

Al-Asasfeh, A., N. Hamdan, and Z. Abo-Hammour. "Flight Control Laws Verification Using Continuous Genetic Algorithms." ISRN Robotics 2013 (March 27, 2013): 1–20. http://dx.doi.org/10.5402/2013/496457.

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This work is concerned with the application of a continuous genetic algorithm (CGA) to solve the nonlinear optimization problem that results from the clearance process of nonlinear flight control laws. The CGA is used to generate a pilot command signal that governs the aircraft performance around certain points in the flight envelope about which the aircraft dynamics were trimmed. The performance of the aircraft model due to pitch and roll pilot commands is analyzed to find the worst combination that leads to a nonallowable load factor. The motivations for using the CGA to solve this type of optimization problem are due to the fact that the pilot command signals are smooth and correlated, which are difficult to generate using the conventional genetic algorithm (GA). Also the CGA has the advantage over the conventional GA method in being able to generate smooth solutions without the loss of significant information in the presence of a rate limiter in the controller design and the time delay in response to the actuators. Simulation results are presented which show superior convergence performance using the CGA compared with conventional genetic algorithms.

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18

Campa, G., S. Wan, M. R. Napolitano, B. Seanor, and M. L. Fravolini. "Design of formation control laws for manoeuvred flight." Aeronautical Journal 108, no. 1081 (2004): 125–34. http://dx.doi.org/10.1017/s0001924000151577.

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Abstract This paper presents identification, control synthesis and simulation results for an YF-22 aircraft model designed, built, and instrumented at West Virginia University. The ultimate goal of the project is the experimental demonstration of formation flight for a set of 3 of the above models. In the planned flight configuration, a pilot on the ground maintains controls of the leader aircraft while a wingman aircraft is required to maintain a pre-defined position and orientation with respect to the leader. The identification of both a linear model and a nonlinear model of the aircraft from flight data is discussed first. Then, the design of the control scheme is presented and discussed with an emphasis on the amount of information, relative to the leader aircraft, needed by the wingman to maintain formation. Using the developed nonlinear model, the control laws for a maneuvered flight of the formation are then simulated with Simulink® and displayed with the Virtual Reality Toolbox®. Simulation studies have been performed to evaluate the effects of specific parameters and the system robustness to atmospheric turbulence. The conclusions from this analysis have allowed the formulation of specific guidelines for the design of the electronic payload for formation flight.

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19

Ostojic, Mile. "Numerical Approach to Nonlinear Control Design." Journal of Dynamic Systems, Measurement, and Control 118, no. 2 (1996): 332–37. http://dx.doi.org/10.1115/1.2802323.

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The paper presents a new approach to designing tracking control of uncertain nonlinear plants. The approach is entirely based on numerical methods and corresponding recurrence relations. It results in recursive control laws that resolve plant nonlinearities and compensate all disturbances and parameter variations. Also, it enables a free shaping of the control error dynamics. Control algorithms based on the method of successive substitutions and the Newton’s method are studied in detail. Detailed description of an application and experimental evaluation is included.

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20

Siddikov, Isamidin, Davronbek Khalmatov, and Dilnoza Khushnazarova. "Synthesis of synergetic laws of control of nonlinear dynamic plants." E3S Web of Conferences 452 (2023): 06024. http://dx.doi.org/10.1051/e3sconf/202345206024.

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Given in the work the facilities of applying the methods of the synergistic approach for the synthesis of the law of control of nonlinear dynamic plants. To give, robust properties of the control law were proposed by applying a principle of integral adaptation, which permitted compensation for the impact of the external and parametric disturbances. The realization synergistic law of control is carried out by when constructing the analytical design of aggregated controllers, which procure asymptotic sustainability of the control system for nonlinear dynamic plants. For procuring technological invariance proposed principle of the synergistic control. Formulated an extended dynamical model of the system, which included external and internal disturbances. The essence of proposing the approach is to use an extended model of the plant, taking into account disturbances due to the switching on of integrators and procuring compensation for the influence of disturbances, in distinction from known ones, where uses separate models for each disturbance. The suggested methodology has confirmed examples of digital simulation and has shown an efficient proposed approach to tasks synthesis of a nonlinear system of control with dynamical plants, procuring asymptotic sustainability of the control system and recouping unmeasured and internal disturbance.

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21

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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22

Wang, Rongdong, and Reza Ahangar. "Computational Approach to Control Laws of Strict-Feedback Nonlinear Systems." OALib 03, no. 10 (2016): 1–12. http://dx.doi.org/10.4236/oalib.1102938.

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23

Menon, Prathyush P., Jongrae Kim, Declan G. Bates, and Ian Postlethwaite. "Clearance of Nonlinear Flight Control Laws Using Hybrid Evolutionary Optimization." IEEE Transactions on Evolutionary Computation 10, no. 6 (2006): 689–99. http://dx.doi.org/10.1109/tevc.2006.873220.

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24

Fang, Y., W. E. Dixon, D. M. Dawson, and E. Zergeroglu. "Nonlinear coupling control laws for an underactuated overhead crane system." IEEE/ASME Transactions on Mechatronics 8, no. 3 (2003): 418–23. http://dx.doi.org/10.1109/tmech.2003.816822.

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25

Yang, Shaofu, Jun Wang, and Qingshan Liu. "Consensus of Heterogeneous Nonlinear Multiagent Systems With Duplex Control Laws." IEEE Transactions on Automatic Control 64, no. 12 (2019): 5140–47. http://dx.doi.org/10.1109/tac.2019.2912533.

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26

Aranda-Bricaire, Eduardo, and Sergej Čelikovský. "Design of Continuous Stabilizing Control Laws for Nonlinear Triangular Systems." IFAC Proceedings Volumes 31, no. 18 (1998): 77–82. http://dx.doi.org/10.1016/s1474-6670(17)41970-7.

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27

Snell, S. A., and P. W. Stout. "Improved Robustness for Dynamic Inversion Based Nonlinear Flight Control Laws." IFAC Proceedings Volumes 27, no. 13 (1994): 261–66. http://dx.doi.org/10.1016/s1474-6670(17)45810-1.

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28

Fagiano, Lorenzo, Massimo Canale, and Mario Milanese. "Set membership approximation of discontinuous nonlinear model predictive control laws." Automatica 48, no. 1 (2012): 191–97. http://dx.doi.org/10.1016/j.automatica.2011.09.039.

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29

Alhazmi, Khalid, and S. Mani Sarathy. "Improving Nonlinear Model Predictive Control Laws via Implicit Q-Learning." IFAC-PapersOnLine 56, no. 2 (2023): 10027–32. http://dx.doi.org/10.1016/j.ifacol.2023.10.869.

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30

Xakimovich, Siddikov Isomiddin, and Umurzakova Dilnoza Maxamadjanovna. "Optimal control of the dynamics of nonlinear oscillating systems using synergetic principles of self-organization." International Journal of Electrical and Computer Engineering (IJECE) 14, no. 6 (2024): 6271. http://dx.doi.org/10.11591/ijece.v14i6.pp6271-6278.

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This paper analyses the evolution of nonlinear oscillation control methods and presents an innovative approach known as analytical design of aggregated oscillation controllers (ADACO). This method is based on the principles of synergetic control theory and focuses on the integration of self-organization and control processes to synthesize energy-efficient control laws for nonlinear oscillating systems. The authors elaborate on the theoretical foundations of ADACO, which extends the previous analytical design of aggregated controllers (ADAC) method by incorporating energy invariants and integrals of motion into the synthesis of control laws. This approach demonstrates significant advantages over traditional methods, offering a versatile framework for the design of energy-efficient control systems for a wide range of nonlinear oscillating systems in various fields such as aerospace, robotics, vibromechanical systems, and objects with chaotic dynamics. The aim of the paper is to establish a unified approach to the control of nonlinear oscillations, solving both the problems of generation of stable oscillations and suppression of unwanted perturbations. The application of synergetic control principles in the framework of ADACO opens prospects for further development of nonlinear control theory.

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31

Richard, E., and S. Scavarda. "Comparison Between Linear and Nonlinear Control of an Electropneumatic Servodrive." Journal of Dynamic Systems, Measurement, and Control 118, no. 2 (1996): 245–52. http://dx.doi.org/10.1115/1.2802310.

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In the robotics field control laws taking into account the nonlinearities caused by the mechanical structure have been proposed, assuming that the drive system is linear. These control laws are well-adapted to the case of electric actuators. Electrohydraulics or electropneumatics drive systems introduce other nonlinearities coming both from the servo-valve and the actuator. In most cases these nonlinearities are neglected and the control laws usually used for these drive systems are based on a reduced third-order model obtained by a tangent linearization. A more satisfying solution is to introduce the nonlinearities of the drive system in the control law. This paper deals with the nonlinear control of an electropneumatic servodrive and is based on the nonlinear control theory in continuous time. It takes into account the main specific nonlinearities. The proposed control law consists of an exact input-output linearization via a static nonlinear state feedback. In our case, this control law leads to a one-dimensional unobservable subspace in closed-loop. A physical interpretation of this nonlinear control is given. This interpretation enables us to improve the understanding of the behavior of an electropneumatic servodrive. In order to compare the results obtained from an experimental device, the synthesis of a linear control law in discrete and continuous time is presented. A study in discrete time of the root locus versus position of the closed loop system with the linear control law, shows oscillations in the neighbourhood of the end of the actuator stroke. The experimental results confirm this fact. With nonlinear control these oscillations are suppressed.

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32

Konstantinov, O. V. "Control of a reservoir partially filled with liquid based on Gauss's principle of least constraint (deceleration task)." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2019): 86–89. http://dx.doi.org/10.17721/1812-5409.2019/1.19.

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The task of constructing control for the motion of a given reservoir - a liquid with a free surface mechanical system is provided in the presence of constant perturbations - the oscillations of the free surface of the liquid. To construct the control, the principle of the least coaxing of Gauss was used, which allows to minimize the control load and implement the given laws of the software movement. The control calculation was carried out on the basis of a simplified linear model with two degrees of freedom, which allowed the control function to be obtained in analytical form for various software laws (including nonlinear) movement of the reservoir and free surface of the liquid. The tank partially filled with a liquid, which initially moves evenly at a given speed, must be completely stopped at a given time. The control, constructed for the implementation of linear software laws of motion, can be used only to provide "comfortable" movements of the reservoir, that is, in the absence of large disturbances of the free surface of the liquid. In order to ensure the movement of the reservoir in the presence of highly intense loads, it is necessary to introduce nonlinear software motion laws for obtaining and using a nonlinear control law.

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33

Xiao, Wei, Zhixiang Yin, Tianyue Zhou, Zi Ye, and Xiaoqi Yang. "A New Adaptive Controller for Nonlinear Systems with Uncertain Virtual Control Gains." Complexity 2022 (March 28, 2022): 1–21. http://dx.doi.org/10.1155/2022/7408077.

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This paper addresses the adaptive asymptotic tracking control problem for nonlinear systems whose virtual control gains are unknown nonlinear functions of system states. Only in the first step, the Nussbaum gain technique is utilized to handle the uncertain virtual control gain. In the remaining steps, virtual control gains are dealt with by constructing novel control laws without the approximation of the uncertain nonlinear functions and external disturbances by neural networks or fuzzy logic. New adaptive laws are defined to compensate for unknown virtual control gains, uncertain parameters, and external disturbances. Finally, an adaptive tracking controller is designed and applied to the control of a 3-order robot system, which guarantees the boundedness of all the signals in the closed-loop system and asymptotic stability of the tracking error.

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34

Snell, S. A., and P. W. Stout. "Flight Control Law Using Nonlinear Dynamic Inversion Combined With Quantitative Feedback Theory." Journal of Dynamic Systems, Measurement, and Control 120, no. 2 (1998): 208–15. http://dx.doi.org/10.1115/1.2802411.

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A method of designing control laws for uncertain nonlinear systems is presented. Dynamic inversion is used to partially linearize the dynamics and then a nonlinear version of quantitative feedback theory (QFT) is applied to the resulting system which assures robustness to plant uncertainty. The design yields good performance with low bandwidth. An application to the design of flight control laws for a high performance aircraft is presented. The control laws demonstrate good performance by accurately following large angle of attack commands at flight speeds ranging from 53 to 150 m/s. Robustness is verified by including ±20 percent variations in pitching moment derivatives. The reduced bandwidth compared to a fixed-gain, linear design, leads to greatly reduced actuator transients, which should give improved reliability and longer life for the actuators and associated structure.

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35

Kostoglotov, Andrey, Sergey Lazarenko, Alexander Agapov, and Zoya Lyashchenko. "The condition for the maximum of the generalized power function in the problem of forming a multi-mode control law with limitation." E3S Web of Conferences 210 (2020): 01003. http://dx.doi.org/10.1051/e3sconf/202021001003.

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A quasi-optimal control law is developed based on the condition for the maxi-mum of the generalized power function taking into account the stationarity of the Hamiltonian on the switching line for control objects that can be represented by the Lagrange equations of the second kind. The comparative analysis is carried out based on the mathematical simulation using the optimal nonlinear control laws with respect to several criteria. We found that the modes of the proposed control law provide high accuracy of approximation to the optimal performance laws and the Fuller laws, reducing energy costs for control by eliminating more frequent switching. The choice of the parameters of the developed control law makes it possible to implement a wide range of both nonlinear and linear operating modes, which allows to classify the obtained control law as multimode law.

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36

Zong, Xiao Ping, Miao Zhang, and Pei Guang Wang. "Adaptive Controller Design for SISO Switched Nonlinear Systems with Linear Uncertain Parameters." Applied Mechanics and Materials 602-605 (August 2014): 1362–66. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.1362.

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This paper presents that single input single output (SISO) switched nonlinear system tracks the variation of the state error to approach the excepted values by using model reference adaptive control (MRAC) method. In order to improve the adaptive control for nonlinear systems by Using Narendra method and dividing the system into two parts: linear and nonlinear parts. The controllers are designed to guarantee that the systems are closed to the model reference system with the arbitrary switching signal. Switching systems can ensure choose the best controller so that can enhance the performance. The adaptive laws are given that are based on a class of feedback single input single output nonlinear uncertain systems which can switch feedback linear standard models. The adaptive laws are different from the classic adaptive laws, because they vary with different switching signals until the best matching one comes. Simulation results show that the proposed method is effective.

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37

Eryilmaz, Bora, and Bruce H. Wilson. "Improved Tracking Control of Hydraulic Systems." Journal of Dynamic Systems, Measurement, and Control 123, no. 3 (1999): 457–62. http://dx.doi.org/10.1115/1.1386394.

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Tracking control for hydraulic systems is a key system requirement, as these devices must often follow prescribed motions. Tracking control of hydraulic systems has been approached using both linear and nonlinear control laws. The latter provides improved performance, but at the expense of additional sensors. Further, the control laws often employ hydraulic fluid bulk modulus—a difficult-to-characterize quantity—as a parameter. To overcome these difficulties, we have developed a control design procedure that requires no additional sensors and is robust to variations in the bulk modulus. A dual approach of singular perturbation theory and Lyapunov techniques form the basis for the procedure. For the cases of a small-amplitude sinusoidal input and large-amplitude polynomial input, a candidate system achieved good tracking performance and exhibited outstanding robustness. The ability to accomplish good tracking in a robust manner with no additional sensors provides advantages over other nonlinear tracking algorithms.

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38

ud Din, Sami, Qudrat Khan, Fazal ur Rehman, and Rini Akmeliawati. "Robust Control of Underactuated Systems: Higher Order Integral Sliding Mode Approach." Mathematical Problems in Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/5641478.

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This paper presents a robust control design for the class of underactuated uncertain nonlinear systems. Either the nonlinear model of the underactuated systems is transformed into an input output form and then an integral manifold is devised for the control design purpose or an integral manifold is defined directly for the concerned class. Having defined the integral manifolds discontinuous control laws are designed which are capable of maintaining sliding mode from the very beginning. The closed loop stability of these systems is presented in an impressive way. The effectiveness and demand of the designed control laws are verified via the simulation and experimental results of ball and beam system.

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39

Wen, J., and A. A. Desrochers. "An Algorithm for Obtaining Bang-Bang Control Laws." Journal of Dynamic Systems, Measurement, and Control 109, no. 2 (1987): 171–75. http://dx.doi.org/10.1115/1.3143835.

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Bang-bang control problems have long been of interest to control engineers. Much of the theoretical study of these problems has been limited to linear systems and the results are usually problem-specific. This paper presents a new computational method for solving control problems when it is desired that the control action be bang-bang. A gradient-based algorithm is developed where the switching times are updated to minimize the final state missed distance. The algorithm explains how a change in a switching time propagates through the other switching times and affects the final state. The algorithm is applicable to linear and nonlinear problems, including multi-input systems.

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40

Nikitin, Denis, Carlos Canudas-de-Wit, and Paolo Frasca. "Shape-Based Nonlinear Model Reduction for 1D Conservation Laws." IFAC-PapersOnLine 53, no. 2 (2020): 5309–14. http://dx.doi.org/10.1016/j.ifacol.2020.12.1216.

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41

Sedlmair, Nicolas, Julian Theis, and Frank Thielecke. "Experimental Comparison of Nonlinear Guidance Laws for Unmanned Aircraft." IFAC-PapersOnLine 53, no. 2 (2020): 14805–10. http://dx.doi.org/10.1016/j.ifacol.2020.12.1922.

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42

Chiaramonti, M., and G. Mengali. "Control laws for a formation of autonomous flight vehicles." Aeronautical Journal 113, no. 1147 (2009): 609–16. http://dx.doi.org/10.1017/s0001924000003274.

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Abstract This paper investigates the performance of a flight control system, based on nonlinear dynamics inversion theory, whose aim is to maintain a given geometry of a formation of unmanned aerial vehicles. A fundamental aspect is the complete three dimensionality of the formation geometry that provides a substantial improvement over existing two-dimensional control laws. The designed control system has been implemented in a Simulink® environment and its effectiveness has been tested with a campaign of numerical simulations.

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43

Rincon, Alejandro, and Fabiola Angulo. "Adaptive Control for Nonlinear Systems with Time-Varying Control Gain." Journal of Control Science and Engineering 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/269346.

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We propose a scheme for nonlinear plants with time-varying control gain and time-varying plant coefficients, on the basis of a plant model consisting of a Brunovsky-type model with polynomials as approximators. We develop an adaptive robust control scheme for this plant, under the following assumptions: (i) the plant terms involve time-varying but bounded coefficients, being its upper bound unknown; (ii) the control gain is unknown, not necessarily bounded, and only its signum is known. To achieve robustness, we use a combination of robustifying control inputs and dead zone-type update laws. We apply this methodology to the speed control of a permanent magnet synchronous motor (PMSM), and we achieve proper tracking results.

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Meng, Guang Lei. "Control Architecture and Control Laws Design for Multiple UAVs Formation Flight." Applied Mechanics and Materials 246-247 (December 2012): 853–57. http://dx.doi.org/10.4028/www.scientific.net/amm.246-247.853.

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An autonomous formation-flight method for multiple UAVs (Unmanned Aerial Vehicle) was designed. First the mathematical representation of formation shape was analyzed. Then the control architecture was devised for multiple UAVs formation flight based on finite state machine. The flight states of the wing UAV were built through the formation flight and the transformation relationships of these flight states were defined. So the automated transformation among these flight states could be achieved and the intelligence of the pilots could be mimicked by this way. Aiming at the typical flight state which is capable of maintaining the formation shape, the control laws were contrived for the wing UAVs. Finally, two nonlinear fighter models which have 6 degrees of freedom were selected to carry out autonomous formation-flight experiments. And the results show the control laws designed for maintaining the formation shape are valid.

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Wang, Yonggang, Yujin Lu, and Ruimin Xiao. "Application of Nonlinear Adaptive Control in Temperature of Chinese Solar Greenhouses." Electronics 10, no. 13 (2021): 1582. http://dx.doi.org/10.3390/electronics10131582.

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The system of a greenhouse is required to ensure a suitable environment for crops growth. In China, the Chinese solar greenhouse plays a crucial role in maintaining a proper microclimate environment. However, the greenhouse system is described with complex dynamic characteristics, such as multi-disturbance, parameter uncertainty, and strong nonlinearity. It is difficult for the conventional control method to deal with the above problems. To address these problems, a dynamic model of Chinese solar greenhouses was developed based on energy conservation laws, and a nonlinear adaptive control strategy combined with a Radial Basis Function neural network was presented to deal with temperature control. In this approach, nonlinear adaptive controller parameters were determined through the generalized minimum variance laws, while unmodeled dynamics were estimated by a Radial Basis Function neural network. The control strategy consisted of a linear adaptive controller, a neural network nonlinear adaptive controller, and a switching mechanism. The research results show that the mean errors were 0.8460 and 0.2967, corresponding to a conventional PID method and the presented nonlinear adaptive scheme, respectively. The standard errors of the conventional PID method and the nonlinear adaptive control strategy were 1.8480 and 1.3342, respectively. The experimental results fully prove that the presented control scheme achieves better control performance, which meets the actual requirements.

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Muslimov, T. Z., and R. A. Munasypov. "Decentralized Nonlinear Group Control of Fixed-Wing UAV Formation." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 1 (2020): 43–50. http://dx.doi.org/10.17587/mau.21.43-50.

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The article proposes a control method for autonomous unmanned aerial vehicles (UAVs) group of a fixed-wing type intended to both implement and support flight information with predetermined relative distances between the vehicles. The suggested approach provides any selected geometric formation shape construction and further preservation when UAVs enter a straight-line trajectory described by a given course with arbitrary initial positions of UAVs in the horizontal plane. The proposed method feature is "autopilot—UAV" system’s nonlinear structure consideration, manifesting itself in both the autopilot input commands restrictions existence as well as nonholonomic UAV dynamics. In addition, there is an unlimited multi-UAV system scalability available due to decentralization. We take into account the need to maintain a minimum flight speed of not less than the stall speed and the final speed of the formation equal to the cruising speed of this type of UAV. The nonlinear group control laws synthesized using Lyapunov’s direct method are based on the decentralized consensus interaction topology, initially developed for linear agents, which implies each vehicle to interact with its neighboring vehicles only. Global asymptotic stability for the current control laws has been proved. As a result, proposed control laws determine a non-uniform path-following vector field for each vehicle in the whole UAV group flight space (currently two-dimensional space). The suggested field vector norm at a certain space point is the airspeed command for the vehicle at that point while the vector direction is the course angle command. The proposed approach effectiveness has been successfully tested in the MATLAB/Simulink while using realistic nonlinear six degree-of-freedom (DOF) 12-states fixed-wing UAV models. High fidelity simulation results confirm the suggested approach effectiveness.

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Villaumé, Fabrice, and Matthieu Jeanneau. "CONTROL LAWS FOR AUTOMATIC TAKE-OFF USING ROBUST NONLINEAR INVERSION TECHNIQUES." IFAC Proceedings Volumes 40, no. 12 (2007): 1022–27. http://dx.doi.org/10.3182/20070822-3-za-2920.00170.

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Houska, Boris, and Moritz Diehl. "Robust Design of Linear Control Laws for Constrained Nonlinear Dynamic Systems." IFAC Proceedings Volumes 44, no. 1 (2011): 13438–43. http://dx.doi.org/10.3182/20110828-6-it-1002.01771.

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49

Adams, Richard J., James M. Buffington, and Siva S. Banda. "Design of nonlinear control laws for high-angle-of-attack flight." Journal of Guidance, Control, and Dynamics 17, no. 4 (1994): 737–46. http://dx.doi.org/10.2514/3.21262.

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Menon, Prathyush P., Declan G. Bates, and Ian Postlethwaite. "Nonlinear robustness analysis of flight control laws for highly augmented aircraft." Control Engineering Practice 15, no. 6 (2007): 655–62. http://dx.doi.org/10.1016/j.conengprac.2006.11.015.

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