scholarly journals Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1110 ◽  
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Quanmin Zhu ◽  
Maamar Bettayeb ◽  
Giuseppe Fusco ◽  
...  
Keyword(s):  
Robust Control ◽  
Lyapunov Function ◽  
Chaotic System ◽  
Finite Time ◽  
Input Saturation ◽  
Robust Stabilization ◽  
Control Law ◽  
Robust Controller ◽  
Control Lyapunov Function ◽  
Error Variable

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.

scholarly journals Transformation of CLF to ISS-CLF for Nonlinear Systems with Disturbance and Construction of Nonlinear Robust Controller withL2Gain Performance

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Keizo Okano ◽  
Kojiro Hagino ◽  
Hidetoshi Oya
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Feedback Linearization ◽  
Feedback System ◽  
Stability Control ◽  
Control Law ◽  
Robust Controller ◽  
Control Lyapunov Function ◽  
Nonlinear Control Law ◽  
Nonlinear Robust

A new nonlinear control law for a class of nonlinear systems with disturbance is proposed. A control law is designed by transforming control Lyapunov function (CLF) to input-to-state stability control Lyapunov function (ISS-CLF). The transformed CLF satisfies a Hamilton-Jacobi-Isaacs (HJI) equation. The feedback system by the proposed control law has characteristics ofL2gain. Finally, it is shown by a numerical example that the proposed control law makes a controller by feedback linearization robust against disturbance.

Finite-Time Chaos Control of the Chaotic Financial System Based on Control Lyapunov Function

2011 ◽  
Vol 55-57 ◽  
pp. 203-208 ◽  
Author(s):  
Yu Ling Wang ◽  
Jun Hai Ma ◽  
Yu Hua Xu
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Finite Time ◽  
Chaos Control ◽  
Financial System ◽  
Control Law ◽  
Control Lyapunov Function

In this paper, we deal with the finite-time chaos control of the chaotic financial system. Based on the control Lyapunov function (CLF) theory, the control law are proposed to drive chaos to equilibria within finite time. Numerical simulations are given to show the effectiveness of the proposed controller.

scholarly journals Nonlinear robust control of large-scale system with input saturation

2021 ◽  
pp. 13-21
Author(s):  
Eugenie L. Eremin ◽  
Larisa V. Nikiforova ◽  
Evgeniy A. Shelenok
Keyword(s):  
Robust Control ◽  
Large Scale ◽  
Input Saturation ◽  
Control Algorithms ◽  
Control Law ◽  
Multiply Connected ◽  
Robust Control System ◽  
Control Saturation ◽  
Decentralized Robust Control ◽  
Nonlinear Robust

The article studies control algorithms of multiply connected system for dynamic plants with control saturation and nonlinear cross-connections. The authors of the article offer a decentralized control law based on the hyperstability criterion. They also use this law to constuct the MIMO servo system with input saturation. To illustrate the capability of the proposed decentralized robust control system the authors use an inverted pendulums connected by a spring.

Swarming Coordination with Robust Control Lyapunov Function Approach

2013 ◽  
Vol 78 (3-4) ◽  
pp. 499-515 ◽  
Author(s):  
Soon Hooi Chiew ◽  
Weihua Zhao ◽  
Tiauw Hiong Go
Keyword(s):  
Robust Control ◽  
Lyapunov Function ◽  
Function Approach ◽  
Control Lyapunov Function

Multiobjective Robust Controller Synthesis for Nonlinear Mechanical System

2018 ◽  
Vol 19 (11) ◽  
pp. 691-698 ◽  
Author(s):  
G. L. Degtyarev ◽  
R. N. Faizutdinov ◽  
I. O. Spiridonov
Keyword(s):  
Robust Control ◽  
Control Theory ◽  
Mechanical System ◽  
Controller Design ◽  
Controller Synthesis ◽  
Control Law ◽  
Robust Controller ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System ◽  
Robust Control Theory

In the paper multiobjective robust controller synthesis problem for nonlinear mechanical system described by Lagrange’s equations of the second kind is considered. Such tasks have numerous practical applications, for example in controller design of robotic systems and gyro-stabilized platforms. In practice, we often have to use uncertain mathematical plant models in controller design. Therefore, ensuring robustness in presence of parameters perturbations and unknown external disturbances is an important requirement for designed systems. Much of modern robust control theory is linear. When the actual system exhibits nonlinear behavior, nonlinearities are usually included in the uncertainty set of the plant. A disadvantage of this approach is that resulting controllers may be too conservative especially when nonlinearities are significant. The nonlinear H∞ optimal control theory developed on the basis of differential game theory is a natural extension of the linear robust control theory. Nonlinear theory methods ensure robust stability of designed control systems. However, to determine nonlinear H∞-control law, the partial differential equation have to be solved which is a rather complicated task. In addition, it is difficult to ensure robust performance of controlled processes when using this method. In this paper, methods of linear parameter-varying (LPV) systems are used to synthesize robust control law. It is shown, that Lagrange system may be adequately represented in the form of quasi-LPV model. From the computational point of view, the synthesis procedure is reduced to convex optimization techniques under constraints expressed in the form of linear matrix inequalities (LMIs). Measured parameters are incorporated in the control law, thus ensuring continuous adjustment of the controller parameters to the current plant dynamics and better performance of control processes in comparison with H∞-regulators. Furthermore, the use of the LMIs allows to take into account the transient performance requirements in the controller synthesis. Since the quasi-LPV system depends continuously on the parameter vector, the LMI system is infinite-dimensional. This infinitedimensional system is reduced to a finite set of LMIs by introducing a polytopic LPV representation. The example of multiobjective robust control synthesis for electro-optical device’s line of sight pointing and stabilization system suspended in two-axes inertially stabilized platform is given.

scholarly journals Adaptive Control Design for Arneodo Chaotic System with Uncertain Parameters and Input Saturation

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chunhua Cheng ◽  
Fengjuan Gao ◽  
Jingshuo Xu ◽  
Yuanxin Wang ◽  
Tao Yuan
Keyword(s):  
Chaotic System ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Tracking Control ◽  
Input Saturation ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Uncertain Parameters ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking

In this paper, tracking controller and synchronization controller of the Arneodo chaotic system with uncertain parameters and input saturation are considered. An adaptive tracking control law and an adaptive synchronization control law are proposed based on backstepping and Lyapunov stability theory. The adaptive laws of the unknown parameters are derived by using the Lyapunov stability theory. To handle the effect caused by the input saturation, an auxiliary system is used to compensate the tracking error and synchronization error. The proposed adaptive tracking control and synchronization schemes ensure the effects of tracking and synchronization. Several examples have been detailed to illuminate the design procedure.

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