Stabilization of max-plus-linear systems using model predictive control: The unconstrained case

• Published in: Automatica (Oxford) Vol. 44; no. 4; pp. 971 - 981
• Main Authors: Necoara, Ion, van den Boom, Ton J.J., De Schutter, Bart, Hellendoorn, Hans
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-04-2008; Elsevier
• Subjects: Applied sciences; Bounded buffer stability; Computer science; control theory; systems; Control theory. Systems; Discrete-event systems; Exact sciences and technology; Lyapunov stability; Max-plus-linear systems; Model predictive control; Lyapunov stability; Model predictive control; Bounded buffer stability; Max-plus-linear systems; Discrete-event systems; Stabilization; Non linear control; Dynamical system; Buffer system; Modeling; Due date; Closed feedback; Finite horizon; Reactive system; Linear system; Just in time; Max plus algebra; State constraint; Lyapunov function; Discrete event system
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2007.09.010

Max-plus-linear (MPL) systems are a class of event-driven nonlinear dynamic systems that can be described by models that are “linear” in the max-plus algebra. In this paper we derive a solution to a finite-horizon model predictive control (MPC) problem for MPL systems where the cost is designed to provide a trade-off between minimizing the due date error and a just-in-time production. In general, MPC can deal with complex input and states constraints. However, in this paper we assume that these are not present and it is only required that the input should be a nondecreasing sequence, i.e. we consider the “unconstrained” case. Despite the fact that the controlled system is nonlinear, by employing recent results in max-plus theory we are able to provide sufficient conditions such that the MPC controller is determined analytically and moreover the stability in terms of Lyapunov and in terms of boundedness of the closed-loop system is guaranteed a priori.