Model-Based Reinforcement Learning for Optimal Feedback Control of Switched Systems

This paper examines the use of reinforcement learning-based controllers to approximate multiple value functions of specific classes of subsystems while following a switching sequence. Each subsystem may have varying characteristics, such as different cost or different system dynamics. Stability of the overall switching sequence is proven using Lyapunov-based analysis techniques. Specifically, Lyapunov-based methods are developed to prove boundedness of individual subsystems and to determine a minimum dwell-time condition to ensure stability of the overall switching sequence. Uniformly ultimately bounded regulation of the states, approximation of the value function, and approximation of the optimal control policy is achieved for arbitrary switching sequences provided the minimum dwell-time condition is satisfied.