Mode scheduling under dwell time constraints in switched-mode systems

This paper presents an algorithmic technique for optimal mode scheduling in switched-mode dynamical systems under the constraint of a minimum dwell time. The technique is based on an optimal control formulation of the problem and on narrowing the optimality gap associated with the maximum principle. It consists of the following four successive steps: (i) solving the relaxed optimal control problem; (ii) approximating the relaxed solution by a switched-mode control; (iii) modifying the switched-mode schedule to incorporate the dwell-time constraints; and (iv) improving on the solution obtained in (iii) by further modifying the switching times of the modes. The main innovations of the paper are in the incorporation of the dwell-time constraints in step (iii), and in combining all four steps in a coherent framework. Despite the growing literature on switched-mode optimal control there hardly have emerged general-purpose algorithms which address dwell-time constraints. This paper presents an initial study of our proposed approach and demonstrates its efficacy via simulation examples while deferring theoretical studies to future research.