The Estimation and Optimization of LQR Control for Markovian Jump Systems

This paper addresses the Linear Quadratic Regulator (LQR) control problem for Markovian Jump Systems (MJSs), focusing on estimation and optimization. The challenge lies in the stochastic switching process affecting system states and inputs. The paper proposes an innovative LQR estimation scheme using the Algebraic Riccati Equation (ARE) to derive the optimal control strategy. It then explores LQR optimization, especially when real-time data is unavailable, aiming to minimize the objective function. A generic controller is designed with sampling behavior and mode separation techniques to reduce the number of controllers. The Deep Deterministic Policy Gradient (DDPG) algorithm optimizes the parameters, and numerical experiments show significant performance improvements in the absence of real-time data.