Policy iteration for H∞ control of polynomial time-varying systems

This paper studies the H_∞ control problem for polynomial time-varying systems. The H_∞ control problem has been much less investigated for time-varying systems in comparison to the time-invariant systems. Approximate dynamic programming (ADP) is an optimal method to solve the control problems. Therefore, it is valuable to solve the polynomial time-varying H_∞ control problem with the ADP approach. Considering the time as an independent variable for sum-of-squares (SOS) optimization problems, an SOS-based ADP method is proposed to solve this problem. A policy iteration algorithm is presented, where in its policy evaluation step it is sufficient to solve an optimization problem. Some constraints are added to this optimization problem to guarantee the closed-loop exponential stability. The convergence and stability properties of the proposed algorithm are stated and proven. Moreover, in order to design an H_∞ controller with a smaller disturbance attenuation coefficient, a two-loop algorithm is suggested. Finally, the effectiveness of the proposed method is demonstrated by simulation examples.