A Three-time-scale redesign for robust stabilization and performance recovery of nonlinear systems with input uncertainties

2007 ◽  
Author(s):  
Aranya Chakrabortty ◽  
Murat Arcak
Keyword(s):  
Nonlinear Systems ◽  
Time Scale ◽  
Robust Stabilization ◽  
Performance Recovery ◽  
And Performance ◽  
Input Uncertainties

scholarly journals Robust Stabilization Approach and Performance via Static Output Feedback for a Class of Nonlinear Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Neila Bedioui ◽  
Salah Salhi ◽  
Mekki Ksouri
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Robust Stabilization ◽  
Nonlinear Function ◽  
Static Output Feedback ◽  
Additional Degree ◽  
Lmi Optimization ◽  
And Performance ◽  
The Stability ◽  
Static Output

This paper deals with the stability and stabilization problems for a class of discrete-time nonlinear systems. The systems are composed of a linear constant part perturbated by an additive nonlinear function which satisfies a quadratic constraint. A new approach to design a static output feedback controller is proposed. A sufficient condition, formulated as an LMI optimization convex problem, is developed. In fact, the approach is based on a family of LMI parameterized by a scalar, offering an additional degree of freedom. The problem of performance taking into account an criterion is also investigated. Numerical examples are provided to illustrate the effectiveness of the proposed conditions.

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.

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