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Policy iteration-mode monotone convergence of generalized policy iteration for discrete-time linear systems

This paper presents the properties of policy iteration (PI)-mode monotone convergence and stability of generalized policy iteration (OPI) algorithms for discrete-time (DT) linear systems. OPI is one of the reinforcement learning based dynamic programming (DP) methods for solving optimal control problems, interacting policy evaluation and policy improvement steps. To deal with the convergence and stability of GPI, several equivalent equations are derived. Then, as a result, the PI-mode monotone convergence (one behaves like PI) and stability of GPI algorithm are proved under the some initial conditions which are closely related with Lyapunov approach. Finally, some numerical simulations are performed to verify the proposed convergence and stability properties.