Model predictive control for max-plus-linear discrete event systems

Schutter, Bart De; Boom, T.J.J. van den

doi:10.1016/s0005-1098(01)00054-1

Cited by 251 publications

(126 citation statements)

References 6 publications

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“…In (De Schutter and van den Boom, 2001; Van den Boom and De Schutter, 2004) the MPC framework has been extended to MPL models (1)-(2) as follows. Following the conventional MPC methodology (Rawlings and Mayne, 2009), we define a cost criterion J that reflects the input and output cost functions in the event period…”

Section: Mpc For Stochastic Mpl Systemsmentioning

confidence: 99%

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An Approximation Approach for Model Predictive Control of Stochastic Max-Plus Linear Systems

Farahani

Boom

Weide

et al. 2010

IFAC Proceedings Volumes

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Model Predictive Control (MPC) is a model-based control method based on a receding horizon approach and online optimization. In previous work we have extended MPC to a class of discrete-event systems, namely the max-plus linear systems, i.e., models that are "linear" in the maxplus algebra. Lately, the application of MPC for stochastic max-plus-linear systems has attracted a lot of attention. At each event step, an optimization problem then has to be solved that is, in general, a highly complex and computationally hard problem. Therefore, the focus of this paper is on decreasing the computational complexity of the optimization problem. To this end, we use an approximation approach that is based on the p-th raw moments of a random variable. This method results in a much lower computational complexity and computation time while still guaranteeing a good performance.

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Section: Mpc For Stochastic Mpl Systemsmentioning

confidence: 99%

“…Although conventional MPC uses linear or nonlinear discrete-time model, MPC has also been extended to discrete-event systems (De Schutter and van den Boom, 2001;Necoara et al, 2004).…”

Section: Introductionmentioning

confidence: 99%

An Approximation Approach for Model Predictive Control of Stochastic Max-Plus Linear Systems

Farahani

Boom

Weide

et al. 2010

IFAC Proceedings Volumes

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“…The MPC approach of De Schutter and van den Boom (2001) can cope with stateinput constraints. However, this approach cannot guarantee a priori stability of the closed-loop system.…”

Section: Examplementioning

confidence: 99%

“…In Baccelli et al (1992) it has been shown that a DES with synchronization but no concurrency can be modeled by a max-plus-linear (MPL) system. Although several authors have already developed methods to compute optimal controllers for MPL systems (Baccelli et al 1992;Cofer and Garg 1996;De Schutter and van den Boom 2001;Kumar and Garg 1994;Libeaut and Loiseau 1995;Menguy et al 1997Menguy et al , 2000Necoara 2006), the literature on stabilizing controllers for this class of systems subject to input and state constraints is relatively sparse. Some of the contributions that partially address this problem include model predictive control (MPC; van den Boom 2001, 2006) and optimal control based on residuation theory (Cottenceau et al 2001;Maia et al 2003;Menguy et al 1997Menguy et al , 2000.…”

Section: Introductionmentioning

confidence: 99%

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

Necoara

Schutter

Boom

et al. 2007

Discrete Event Dyn Syst

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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 closedloop 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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“…In (De Schutter and De Moor, 1995b;De Schutter and De Moor, 1997;De Schutter and De Moor, 1998b;De Schutter and van den Boom, 2001) we have shown that many fundamental problems in the max-plus algebra and in max-plus-algebraic system theory for discrete event systems can be solved using the ELCP. More specifically, the following problems can be recast as an ELCP or solved using an ELCP:…”

Section: Max-plus Algebra and The Elcpmentioning

confidence: 99%

Max-Plus-Algebraic Problems and the Extended Linear Complementarity Problem — Algorithmic Aspects

Schutter

Heemels

Bemporad

2002

IFAC Proceedings Volumes

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Many fundamental problems in the max-plus-algebraic system theory for discrete event systems -among which the minimal state space realization problem -can be solved using an Extended Linear Complementarity Problem (ELCP). We present some new, more efficient methods to solve the ELCP. We show that an ELCP with a bounded feasible set can be recast as a standard Linear Complementarity Problem (LCP). Our proof results in three possible numerical solution methods for a given ELCP: regular ELCP algorithms, mixed integer linear programming algorithms, and regular LCP algorithms. We also apply these three methods to a basic max-plus-algebraic benchmark problem.

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Model predictive control for max-plus-linear discrete event systems

Cited by 251 publications

References 6 publications

An Approximation Approach for Model Predictive Control of Stochastic Max-Plus Linear Systems

An Approximation Approach for Model Predictive Control of Stochastic Max-Plus Linear Systems

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

Max-Plus-Algebraic Problems and the Extended Linear Complementarity Problem — Algorithmic Aspects

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