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

Abstract

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 L₂-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 L₂-gain. The efficiency and advantage of the proposed SOS-based algorithm are demonstrated by simulation examples.

KEYWORDS:

• Adaptive dynamic programming (ADP)
• H_∞ control
• parametric robust control
• policy iteration
• sum-of-squares (SOS) optimisation

Disclosure statement

No potential conflict of interest was reported by the author(s).