Optimal robust control and a separation principle for polytopic time-inhomogeneous Markov jump linear systems

Abstract

Markov-jump linear systems (MJLSs) allow representing linear systems subject to abrupt parameter changes modeled as a Markov chain, and are useful in many application domains. In most real cases the transition probabilities between operational modes of such systems cannot be computed exactly and are time-varying. We take into account this aspect by considering MJLSs where the underlying Markov chain is polytopic and time-inhomogeneous, i.e. its transition probability matrix is varying over time with variations that are arbitrary within a polytopic set of stochastic matrices. We address and solve for this class of systems the finite horizon optimal control and filtering problems. In particular, we show that the optimal controller having only partial information on the continuous state can be obtained from two types of coupled Riccati difference equations (CRDEs), one associated to the control problem, and the other one associated to the filtering problem.