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arXiv · 1903.03091

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

Y. Zacchia Lun·A. Abate·A. D'Innocenzo
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Abstract

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 infinite-horizon 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.

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Y. Zacchia Lun, A. Abate, A. D'Innocenzo. 2019-03-07. Linear quadratic regulation of polytopic time-inhomogeneous Markov jump linear systems (extended version). https://doi.org/10.23919/ecc.2019.8796279

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