Optimal Control of Switched-Mode Dynamical Systems

The subject of this presentation is the problem of optimal mode-scheduling in switched-mode hybrid dynamical systems. This problem is cast in the setting of optimal control, where it is desirable to optimize a cost functional, defined on the system's continuous state trajectory, as a function of the schedule of modes. The resultant optimal control problem has a special structure that yields effective iterative algorithms for its solution. This presentation discusses a computational framework that is based on gradient descent and the Armijo step size. The algorithms are analyzed in both off-line and real-time setting, and their convergence is established without assuming an upper bound on the system's switching rate.