Optimal Control of Switched System with Time Delay Detection of Switching Signal

Abstract

This paper deals with optimal control problems governed by switched systems with time delay detection of switching signal. We consider the switching sequence as well as the switching instants as decision variables. We present a two-level optimization method to solve it. In the first level, we fix the switching sequence, and introduce a time scaling transformation such that the switching instants are mapped into pre-assigned fixed knot points. Then, the transformed problem becomes a standard optimal parameter selection problem, and hence can be solved by many optimal control techniques and the corresponding optimal control software packages, such as MISER. In the second level, we consider the switching sequence as decision variables. We introduce a discrete filled function method to search for a global optimal switching sequence. Finally, a numerical example is presented to illustrate the efficiency of our method.