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

Abstract

SummaryThis paper presents a methodology to obtain a guaranteed‐reliability controller for constrained linear systems, 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. Copyright © 2016 John Wiley & Sons, Ltd.