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

  • Authors:

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

  • Affiliations:

  • Delft Center for Systems and Control, Delft University of technology, Delft, Netherlands 2628 CD and Department of Electrical Engineering (ESAT), Katholieke Universiteit Leuven, Leuven-Heverlee, B ...;Delft Center for Systems and Control, Delft University of technology, Delft, Netherlands 2628 CD;Delft Center for Systems and Control, Delft University of technology, Delft, Netherlands 2628 CD;Delft Center for Systems and Control, Delft University of technology, Delft, Netherlands 2628 CD

  • Venue:
  • Discrete Event Dynamic Systems
  • Year:
  • 2007

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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.