(Georgia Institute of Technology, 2015-12)
Wardi, Yorai Y.; Egerstedt, Magnus B.; Hale, M.
This paper concerns optimal mode-scheduling in autonomous switched-mode hybrid dynamical systems, where the objective is to minimize a cost-performance functional defined on the state trajectory as a function of the schedule of modes. The controlled variable, namely the modes’ schedule, consists of the sequence of modes and the switchover times between them. We propose a gradient-descent algorithm that adjusts a given mode-schedule by changing multiple modes over time-sets of positive Lebesgue measures, thereby avoiding the inefficiencies inherent in existing techniques that change the modes one at a time. The algorithm is based on steepest descent with Armijo step sizes along Gˆateaux differentials of the performance functional with respect to schedule-variations, which yields effective descent at each iteration. Since the space of mode-schedules is infinite dimensional and incomplete, the algorithm’s convergence is proved in the sense of Polak’s framework of optimality functions and minimizing sequences. Simulation results are presented, and possible extensions to problems with dwelltime lower-bound constraints are discussed.
(Georgia Institute of Technology, 2005-07)
Boccadoro, Mauro; Egerstedt, Magnus B.; Wardi, Yorai Y.
This paper studies the problem of letting an autonomous mobile robot
negotiate obstacles in an optimal manner. In particular, a multi-modal control
problem is addressed, where different modes of operation control the robot at
different locations in the state space. The specification of the optimal discrete
event dynamics is pursued through the design of optimal, parametrized switching
surfaces, using results on switching surface optimization.