Model-free optimal control of discrete-time systems with additive and multiplicative noises

TL;DR

This paper develops a model-free reinforcement learning method for optimal control of discrete-time stochastic systems with both additive and multiplicative noises, without needing system model knowledge.

Contribution

It introduces a novel model-free RL algorithm for such systems and proves its convergence to the optimal control policy.

Findings

Algorithm converges to optimal policy

Outperforms existing policy iteration methods

Effective in numerical simulations

Abstract

This paper investigates the optimal control problem for a class of discrete-time stochastic systems subject to additive and multiplicative noises. A stochastic Lyapunov equation and a stochastic algebra Riccati equation are established for the existence of the optimal admissible control policy. A model-free reinforcement learning algorithm is proposed to learn the optimal admissible control policy using the data of the system states and inputs without requiring any knowledge of the system matrices. It is proven that the learning algorithm converges to the optimal admissible control policy. The implementation of the model-free algorithm is based on batch least squares and numerical average. The proposed algorithm is illustrated through a numerical example, which shows our algorithm outperforms other policy iteration algorithms.