Stable Model Predictive Control for Constrained Max-Plus-Linear Systems

Reference

I. Necoara, B. De Schutter, T.J.J. van den Boom, and H. Hellendoorn, "Stable Model Predictive Control for Constrained Max-Plus-Linear Systems," Discrete Event Dynamic Systems: Theory and Applications, vol. 17, no. 3, pp. 329-354, Sept. 2007.

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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Bibtex entry

@article{NecDeS:06-023,
author={I. Necoara and B. {D}e Schutter and T.J.J. van den Boom and H. Hellendoorn},
title={Stable Model Predictive Control for Constrained Max-Plus-Linear Systems},
journal={Discrete Event Dynamic Systems: Theory and Applications},
volume={17},
number={3},
pages={329--354},
month=sep,
year={2007},
doi={10.1007/s10626-007-0015-2}
}

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