Risk-sensitive and Robust Control of Discrete Time Hybrid Systems

In this paper we study systems that are subject to sudden structural changes due to either changes in the operational mode of the system or due to failure. We consider linear dynamical that depend on a modal variable which is either modeled as a finite state Markov chain or generated by an automaton that is subject to an external disturbance. In the Markov chain case the objective of the control is to minimize a risk sensitive cost functional. The risk sensitive cost functional measures the risk sensitivity of the system to transitions caused by the random modal variable. In the case when a disturbed automaton describes the modal variable, the objective of the control is to make the system as robust to changes in the external disturbance as possible. Optimality conditions for both problems are derived and it is shown that the disturbance rejection problem is closely related to a certain risk sensitive control problem for the hybrid system.