Reliability and time-to-failure bounds for discrete-time constrained Markov jump linear systems

Abstract

[EN] This paper presents a methodology to obtain a guaranteed-reliability controller for constrained linear sys- tems, which switch between different modes according to a Markov chain (Markov jump linear systems). Inside the classical maximal robust controllable set, there is 100% guarantee of never violating constraints at future time. However, outside such set, some sequences might make hitting constraints unavoidable for some disturbance realisations. A guaranteed-reliability controller based on a greedy heuristic approach was proposed in an earlier work for disturbance-free, robustly stabilisable Markov jump linear systems. Here, extensions are presented by, first, considering bounded disturbances and, second, presenting an iterative algorithm based on dynamic programming. In non-stabilisable systems, reliability is zero; therefore, prior results cannot be applied; in this case, optimisation of a mean-time-to-failure bound is proposed, via minor algorithm modifications. Optimality can be proved in the disturbance-free, finitely generated case.