**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.

Online version of the paper

Corresponding technical report: pdf file (264 KB)

@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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