Optimal Control and Scheduling of Switched Systems

This technical note addresses optimal control and scheduling (controlled switching) of discrete-time switched linear systems. A receding-horizon control and scheduling (RHCS) problem is introduced and solved by dynamic programming, leading to a combinatorial optimization problem with exponential complexity. By relaxed dynamic programming, complexity is reduced while relaxing optimality within prespecified bounds. The resulting RHCS strategy is expressed explicitly as a piecewise linear state feedback control law defined over regions implied by quadratic forms. Closed-loop stability is not guaranteed inherently for the RHCS strategy. Therefore, a posteriori stability criteria based on piecewise quadratic Lyapunov functions are proposed. Finally, a region-reachability criterion is presented.