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

[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.The authors gratefully acknowledge the financial support of Spanish MINECO (DPI2011-27845-C02-01, FPU12/02107) and Generalitat Valenciana (PrometeoII/2013/004).Hernandez-Mejias, MA.; Sala, A. (2017). Reliability and time-to-failure bounds for discrete-time constrained Markov jump linear systems. International Journal of Robust and Nonlinear Control. 27:1773-1791. https://doi.org/10.1002/rnc.3635S177317912

Stochastic model predictive control for constrained discrete-time Markovian switching systems

© 2014 Elsevier Ltd. All rights reserved. In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the SMPC law under very weak assumptions. In the special but important case of constrained MJLS we present an algorithm for computing explicitly the SMPC control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization.publisher: Elsevier articletitle: Stochastic model predictive control for constrained discrete-time Markovian switching systems journaltitle: Automatica articlelink: http://dx.doi.org/10.1016/j.automatica.2014.08.031 content_type: article copyright: Copyright © 2014 Elsevier Ltd. All rights reserved.status: publishe

Stochastic model predictive control for constrained discrete-time Markovian switching systems

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the {SMPC} law under very weak assumptions. In the special but important case of constrained {MJLS} we present an algorithm for computing explicitly the {SMPC} control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization