| This thesis considers the problem of scheduling events of a switched system so that an optimal performance is achieved. Two problems are considered: optimizing the switching times with a fixed mode sequence and optimizing the full mode schedule. Efficient calculations for the switching time gradient and Hessian are given. Furthermore, the switching time optimization problem for time-varying linear switched systems subject to quadratic cost is formulated so that only a single set of differential equations need to be solved prior to optimization. As for the mode scheduling problem, the presented approach has guarantees on convergence and computational complexity which 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 our algorithm returns a dynamically feasible solution such that switching time optimization is applicable. A large class of problems call for optimal mode scheduling, including calculating the timing of discrete changes to the parameters of a multimachine power network for synchronization, which is the concluding example in the thesis. |
