Robust control of discrete-time hybrid systems with uncertain modal dynamics

摘要

We study systems that are subject to sudden structural changesdue to either changes in the operational mode of the system orfailure. We consider linear dynamicalsystems that depend on amodal variable which is either modeled as a finite-state Markovchain or generated by an automaton that is subject to an externaldisturbance. In the Markov chain case, the objective of thecontrol is to minimize a risk-sensitive cost functional. Therisk-sensitive cost functional measures the risk sensitivity ofthe system to transitions caused by the random modal variable. Inthe case when a disturbed automaton describes the modal variable,the objective of the control is to make the system as robust tochanges in the external disturbance as possible. Optimalityconditions for both problems are derived and it is shown that thedisturbance rejection problem is closely related to a certainrisk-sensitive control problem for the hybrid system.