Optimal scheduling for reference tracking or state regulation using reinforcement learning

The problem of optimal control of autonomous nonlinear switching systems with infinite-horizon cost functions, for the purpose of tracking a family of reference signals or regulation of the states, is investigated. A reinforcement learning scheme is presented which learns the solution and provides scheduling between the modes in a feedback form without enforcing a mode sequence or a number of switching. This is done through a value iteration based approach. The convergence of the iterative learning scheme to the optimal solution is proved. After answering different analytical questions about the solution, the learning algorithm is presented. Finally, numerical analyses are provided to evaluate the performance of the developed technique in practice.