On-line adaptive optimal timing control of switched systems

In this paper we consider the problem of optimizing over the switching times for a multi-modal dynamic system when the complete cost-to-go is not available. The instantaneous cost is assumed to be unavailable before run-time, but can be measured in real time. Since the cost-to-go for optimization is time-varying, this problem falls under the category of on-line optimization of switched systems. The goal of the paper is to present an iterative process to update the switching times for the system in such a way that they remain optimal with respect to the changing cost-to-go function. It is shown that the information required to update the switching times is the `rate of change´ of the instantaneous cost, which is in the form of the partial derivative of the instantaneous cost function.