Optimal control of switched dynamical systems under dwell time constraints

This paper addresses the problem of optimally scheduling the mode sequence and mode duration for switched dynamical systems under dwell time constraints that describe how long a system has to stay in a mode before they can switch to another mode. The schedule should minimize a given cost functional defined on the state trajectory. The topology of the optimization space for switched dynamical systems with and without dwell time constraints is investigated and it is shown that the notion of local optimality must be replaced by stationarity with regards to a suitably chosen optimality function when dwell time constraints are present. Hence, an optimality function is proposed to characterize the solution to the dwell time problem as points that satisfy optimality condition defined in terms of optimality function. A conceptual algorithm is presented to solve the mode scheduling problem and its convergence to stationary points is proved. A numerical example is given to highlight the algorithm.