Discrete Event Dynamic Systems

, Volume 17, Issue 3, pp 329–354 | Cite as

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

  • Ion Necoara
  • Bart De Schutter
  • Ton J. J. van den Boom
  • Hans Hellendoorn


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.


Discrete-event systems Max-plus-linear systems Input-state constraints Model predictive control Stability Positively invariant sets 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Ion Necoara
    • 1
    • 2
  • Bart De Schutter
    • 1
  • Ton J. J. van den Boom
    • 1
  • Hans Hellendoorn
    • 1
  1. 1.Delft Center for Systems and ControlDelft University of TechnologyDelftNetherlands
  2. 2.Department of Electrical Engineering (ESAT)Katholieke Universiteit LeuvenLeuven-HeverleeBelgium

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