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

In this paper, we present a new insight into the simultaneous policy update algorithm (SPUA) for solving H-infinity 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-infinity 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. (C) 2019 Elsevier Inc. All rights reserved.