New insight into the simultaneous policy update algorithms related to H∞ state feedback control

Abstract

In this paper, we present a new insight into the simultaneous policy update algorithm (SPUA) for solving H∞ control problems. From the perspective of practicability, a checkable criterion is presented for the initialization of SPUAs such that the initial guess can be chosen with clear rules and lie within a local domain of convergence. To further get a better convergence property, a novel initialization is developed such that the starting matrix does not need to lie in a neighborhood of the solution of H∞ control problems in some cases and its convergence is established rigorously by mathematical induction principle. Subsequently, an improved SPUA is proposed, and its model-free variant based on reinforcement learning (RL) is also able to learn the solution online without any system dynamics. Finally, numerical results illustrate the effectiveness of the proposed methods.