Finite-time Control Using Locally Semiconcave Control Lyapunov Function

2020 ◽  
Vol 56 (11) ◽  
pp. 504-513
Author(s):  
Takuya HAYASHI ◽  
Hisakazu NAKAMURA
Keyword(s):  
Lyapunov Function ◽  
Finite Time ◽  
Control Lyapunov Function ◽  
Time Control

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 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 Finite Time Inverse Optimal Stabilization for Stochastic Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiushan Cai ◽  
Yuhang Lin ◽  
Wei Zhang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Closed Loop ◽  
Loop System ◽  
Stochastic Nonlinear Systems ◽  
Control Law ◽  
Closed Loop System ◽  
Control Lyapunov Function ◽  
Optimal Stabilization ◽  
Time Control

This paper deals with finite time inverse optimal stabilization for stochastic nonlinear systems. A concept of the stochastic finite time control Lyapunov function (SFT-CLF) is presented, and a control law for finite time stabilization for the closed-loop system is obtained. Furthermore, a sufficient condition is developed for finite time inverse optimal stabilization in probability, and a control law is designed to ensure that the equilibrium of the closed-loop system is finite time inverse optimal stable. Finally, an example is given to illustrate the applications of theorems established in this paper.

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