MIMO Robust Control via T-S Fuzzy Models for Nonaffine Nonlinear Systems

2007 ◽  
Author(s):  
Wei-Yen Wang ◽  
Li-Chuan Chien ◽  
I-Hsum Li ◽  
Shun-Feng Su
Keyword(s):  
Robust Control ◽  
Nonlinear Systems ◽  
Fuzzy Models ◽  
Nonaffine Nonlinear Systems

scholarly journals Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration

2021 ◽  
Vol 11 (5) ◽  
pp. 2312
Author(s):  
Dengguo Xu ◽  
Qinglin Wang ◽  
Yuan Li
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Policy Iteration ◽  
Control Law ◽  
Globally Asymptotically Stable ◽  
Control Approach ◽  
Input Uncertainties ◽  
Theoretical Results

In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.

scholarly journals A Fuzzy Approach to Robust Control of Stochastic Nonaffine Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Ting-Ting Gang ◽  
Jun Yang ◽  
Qing Gao ◽  
Yu Zhao ◽  
Jianbin Qiu
Keyword(s):  
Nonlinear Systems ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Dynamic Feedback ◽  
Stabilization Problem ◽  
Fuzzy Models ◽  
Quadratic Lyapunov Functions ◽  
Affine Nonlinear Systems ◽  
Semiglobal Stabilization ◽  
Approximation Capability

This paper investigates the stabilization problem for a class of discrete-time stochastic non-affine nonlinear systems based on T-S fuzzy models. Based on the function approximation capability of a class of stochastic T-S fuzzy models, it is shown that the stabilization problem of a stochastic non-affine nonlinear system can be solved as a robust stabilization problem of the stochastic T-S fuzzy system with the approximation errors as the uncertainty term. By using a class of piecewise dynamic feedback fuzzy controllers and piecewise quadratic Lyapunov functions, robust semiglobal stabilization condition of the stochastic non-affine nonlinear systems is formulated in terms of linear matrix inequalities. A simulation example illustrating the effectiveness of the proposed approach is provided in the end.

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