  This paper describes a method for scheduling the events of a switched system
to achieve an optimal performance. The approach has guarantees on convergence
and computational complexity that parallel derivative-based iterative
optimization but in the infinite dimensional, integer constrained setting of
mode scheduling. In comparison to methods relying on mixed integer programming,
the presented approach does not require a priori discretizations of time or
state. Furthermore, in comparison to embedding and relaxation methods, every
iteration of the algorithm returns a dynamically feasible solution. A large
class of problems call for optimal mode scheduling. This paper considers a
vehicle tracking problem and a high dimensional multimachine power network
synchronization problem. For the power network example, both single horizon and
receding horizon approaches prevent instability of the network, and the
receding horizon approach does so at near real-time speeds on a single
processor.
