Optimization of switched-mode systems with switching costs

This paper concerns the problem of optimizing switched-mode hybrid dynamical systems, where it is required to balance the tracking of a reference signal with an attempt to reduce a state-dependent cost-penalty associated with the switchings among the modes. We propose an algorithmic approach to the problem and we illustrate it on a specific example. The investigation has been motivated by design issues in power electronics, where it is desirable to regulate the load current in a switching circuit by controlling the state of a switch. On one hand tighter regulation requires switching at a higher frequency, and on the other hand each switching requires a certain amount of energy. Our algorithmic approach brings together various techniques that we recently have developed for optimizing hybrid systems, and its demonstrated application on a specific example suggests its potential viability in a broader array of problems in power electronics.