On robust control of uncertain linear systems in the absence of matching conditions

2006 ◽  
pp. 15-36
Author(s):  
Harold Stalford
Keyword(s):  
Robust Control ◽  
Linear Systems ◽  
Matching Conditions ◽  
Uncertain Linear Systems

scholarly journals Adaptive optimal control approach to robust tracking of uncertain linear systems based on policy iteration

2021 ◽  
pp. 002029402110071
Author(s):  
Dengguo Xu ◽  
Qinglin Wang ◽  
Yuan Li
Keyword(s):  
Optimal Control ◽  
Robust Control ◽  
Linear Systems ◽  
Tracking Error ◽  
Policy Iteration ◽  
Time Signal ◽  
Tracking Problem ◽  
Robust Tracking ◽  
Control Approach ◽  
Uncertain Linear Systems

In this study, an optimal adaptive control approach is established to solve the robust output tracking problem of a class of continuous time uncertain linear systems based on the policy iteration (PI) in actor-critic algorithm. First, by augmenting the integral variables of the tracking error into state variables, the robust tracking problem is transformed into a robust control problem of an augmented uncertain linear system. It is proven that the robust control law of the augmented system enables the output of the considered system to track a polynomial time signal asymptotically. Second, an optimal control method in the corresponding auxiliary nominal system is established, and based on the Bellman optimality principle, PI algorithms are proposed to solve online tracking controllers for the matched and the mismatched uncertain systems. Finally, for testing the availability of the proposed approach and theoretical results, two numerical experiments are provided.

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