Convergence rate comparison of two data-driven algorithms to stochastic LQR problems

Le résumé fourni par la source

This paper investigates the linear quadratic regulation (LQR) problem for discrete-time stochastic systems (DTSSs) with state-dependent multiplicative noise. Policy iteration (PI) and value iteration (VI) algorithms are proposed to solve the generalised algebraic Riccati equation (GARE) corresponding to the stochastic LQR (SLQR) problem. Furthermore, based on the proposed PI and VI algorithms, a comparative analysis of their convergence rates is conducted. Additionally, when the system dynamics are completely unknown, this paper introduces online model-free versions of the PI and VI algorithms using reinforcement learning (RL) technology to find the optimal control strategy for the SLQR problem. Finally, numerical simulations validate the feasibility of the proposed algorithms and the correctness of the theoretical results.

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