Stable receding horizon control for max-plus-linear systems


Reference:
I. Necoara, B. De Schutter, T.J.J. van den Boom, and J. Hellendoorn, "Stable receding horizon control for max-plus-linear systems," Proceedings of the 2006 American Control Conference, Minneapolis, Minnesota, pp. 4055-4060, June 2006.

Abstract:
We develop a stabilizing receding horizon control (RHC) scheme for the class of discrete-event systems called max-pus-linear (MPL) systems. MPL systems can be described by models that are "linear" in the max-plus algebra, which has maximization and addition as basic operations. In this paper we extend the concept of positively invariant set from classical system theory to discrete-event MPL systems. We define stability for the class of MPL systems in the sense of Lyapunov. For a particular convex piecewise affine cost function and linear input-state constraints the RHC optimization problem can be recast as a linear program. Using a dual-mode approach we are able to prove exponential stability of the RHC scheme. We derive also a constrained time-optimal controller by solving a sequence of parametric linear programs.


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Bibtex entry:

@inproceedings{NecDeS:05-016,
        author={I. Necoara and B. {De Schutter} and T.J.J. {van den Boom} and J. Hellendoorn},
        title={Stable receding horizon control for max-plus-linear systems},
        booktitle={Proceedings of the 2006 American Control Conference},
        address={Minneapolis, Minnesota},
        pages={4055--4060},
        month=jun,
        year={2006}
        }



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