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

In this article, the H-infinity 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-infinity controller with a smaller L-2-gain. The efficiency and advantage of the proposed SOS-based algorithm are demonstrated by simulation examples.