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.

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 Decreasing the Value of Specified Cost Function by Adaptive Controller Based on Modified ACLF for a Class of Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Keizo Okano ◽  
Kojiro Hagino ◽  
Hidetoshi Oya
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Cost Function ◽  
Design Method ◽  
Adaptive Controller ◽  
Control Law ◽  
Control Lyapunov Function ◽  
Nonlinear Adaptive Control ◽  
Hamilton Jacobi Bellman ◽  
Adaptive Control Law

A new nonlinear adaptive control law for a class of uncertain nonlinear systems is proposed. The proposed control law is designed by a modified adaptive control Lyapunov function (ACLF) which satisfies a Hamilton-Jacobi-Bellman (HJB) equation. The modified ACLF is derived from transformation of an ACLF. The proposed control law is different from the inverse optimal one in decreasing the value of a cost function specified by a designer. In this paper, we show a transformation coefficient for an ACLF and a design method of a nonlinear adaptive controller. Finally, it is shown by a numerical simulation that the proposed control law decreases the value of a given cost function and achieves the desirable trajectory.

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