Optimal Control of Two-Dimensional Roesser Model: Solution Based on Reinforcement Learning

This article addresses the infinite-region linear quadratic regulation problem of the discrete two-dimensional (2-D) Roesser model, drawing inspiration from reinforcement learning principles. It introduces a novel proof establishing that expressing the optimal control law in 2-D through state feedback is unattainable. Subsequently, a policy iteration framework is proposed to derive suboptimal state feedback, followed by an exploration of the true optimal policy through value iteration. The efficacy of these methodologies is demonstrated via two numerical examples, enhancing the practical understanding of these innovative approaches.