Algorithm for Optimal Mode Scheduling in Switched Systems

This paper considers the problem of computing the schedule of modes in an autonomous switched dynamical system, that minimizes a cost functional defined on the trajectory of the system's continuous state variable. It proposes an algorithm that modifies a finite but unbounded number of modes at each iteration, whose computational workload at the various iterations appears to be independent on the number of modes being changed. The algorithm is based on descent directions defined by Gateaux differentials of the performance function with respect to variations in mode-sequences, and its convergence to (local) minima is established in the framework of optimality functions and minimizing sequences, devised by Polak for infinite-dimensional optimization problems.