SOS-based policy iteration for H∞ control of polynomial systems with uncertain parameters

In this article, the H ∞ control problem is investigated for polynomial systems with uncertain parameters by utilising an adaptive dynamic programming (ADP) approach. The goal of this problem is to design a controller that stabilises the system and renders the system L 2 -gain less than some disturb...

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Bibliographic Details
Published in:International journal of control 2023-04, Vol.96 (4), p.1053-1066
Main Authors: Pakkhesal, Sajjad, Shamaghdari, Saeed
Format: Article
Language:English
Subjects:
Adaptive dynamic programming (ADP)
Closed loops
control
Control systems design
Controllers
Dynamic programming
Feedback control
H-infinity control
Iterative algorithms
L2 gain
Optimization
Parameter uncertainty
parametric robust control
policy iteration
Polynomials
Robust control
sum-of-squares (SOS) optimisation
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Summary:In this article, the H ∞ control problem is investigated for polynomial systems with uncertain parameters by utilising an adaptive dynamic programming (ADP) approach. The goal of this problem is to design a controller that stabilises the system and renders the system L 2 -gain less than some disturbance attenuation level for all possible values of the uncertain parameters. A policy iteration (PI) algorithm is proposed to approximately solve the Hamilton-Jacobi-Isaacs (HJI) equation based on the sum-of-squares (SOS) optimisation. The convergence of the iterative algorithm and robustness of the closed-loop system with respect to both external disturbances and parametric uncertainties are guaranteed. Moreover, a two-loop iterative algorithm is presented to design a parametric robust H ∞ controller with a smaller L 2 -gain. The efficiency and advantage of the proposed SOS-based algorithm are demonstrated by simulation examples.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2022.2027523