Stable Model Predictive Control for Constrained Max-Plus-Linear Systems |
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Authors: | Ion Necoara Bart De Schutter Ton J. J. van den Boom Hans Hellendoorn |
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Affiliation: | (1) Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD Delft, Netherlands;(2) Present address: Department of Electrical Engineering (ESAT), Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, bus 2446, B-3001 Leuven-Heverlee, Belgium |
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Abstract: | Discrete-event systems with synchronization but no concurrency can be described by models that are “linear” in the max-plus algebra, and they are called max-plus-linear (MPL) systems. Examples of MPL systems often arise in the context of manufacturing systems, telecommunication networks, railway networks, parallel computing, etc. In this paper we provide a solution to a finite-horizon model predictive control (MPC) problem for MPL systems where it is required that the closed-loop input and state sequence satisfy a given set of linear inequality constraints. Although the controlled system is nonlinear, by employing results from max-plus theory, we give sufficient conditions such that the optimization problem that is performed at each step is a linear program and such that the MPC controller guarantees a priori stability and satisfaction of the constraints. We also show how one can use the results in this paper to compute a time-optimal controller for linearly constrained MPL systems. |
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Keywords: | Discrete-event systems Max-plus-linear systems Input-state constraints Model predictive control Stability Positively invariant sets |
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