BEYOND THE CONSTRUCTION OF OPTIMAL SWITCHING SURFACES FOR AUTONOMOUS HYBRID SYSTEMS

In this paper we report of a technique to design optimal feedback control laws for hybrid systems with autonomous (continuous) modes. Existing techniques design the optimal switching surfaces based on a singular sample evolution of the system; hence providing a solution dependent on the initial conditions. On the other hand, the optimal switching times can be found, providing an an open loop control to the system, but those also are dependent on the initial conditions. The technique presented relies on a variational approach, giving the derivative of the switching times with respect to the initial conditions, thus providing a tool to design programs/algorithms generating switching surfaces which are optimal for any possible execution of the system.