Linear quadratic regulation of polytopic time-inhomogeneous Markov jump linear systems (extended version) [article]

Y. Zacchia Lun, A. Abate, A. D'Innocenzo
2019 arXiv   pre-print
In most real cases transition probabilities between operational modes of Markov jump linear systems cannot be computed exactly and are time-varying. We take into account this aspect by considering Markov jump linear systems 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
more » ... rizon optimal control problem. In particular, we show that the optimal controller can be obtained from a set of coupled algebraic Riccati equations, and that for mean square stabilizable systems the optimal finite-horizon cost corresponding to the solution to a parsimonious set of coupled difference Riccati equations converges exponentially fast to the optimal infinite-horizon cost related to the set of coupled algebraic Riccati equations. All the presented concepts are illustrated on a numerical example showing the efficiency of the provided solution.
arXiv:1903.03091v1 fatcat:j64eudp7dvhplj6ik2dmz4o3au