Model reference control for timed event graphs in dioids

Cottenceau, Bertrand; Hardouin, Laurent; Boimond, Jean-Louis; Ferrier, Jean-Louis

doi:10.1016/s0005-1098(01)00073-5

Cited by 103 publications

(90 citation statements)

References 6 publications

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“…F = ε is a solution of (10) (since M (ε) = CA * S), hence the greatest solution, if it exists, also achieves equality. From (10), we seek for the 5 In a manufacturing system, q may represent the supply of raw material which is a priori known. The problem is then very similar to the problem introduced in [9] which establishes an optimal open-loop control in presence of known uncontrollable inputs.…”

Section: Output Feedbackmentioning

confidence: 99%

“…The problem is then very similar to the problem introduced in [9] which establishes an optimal open-loop control in presence of known uncontrollable inputs. 6 We recall that (ab) * a = a(ba) * (see [5] …”

Section: Output Feedbackmentioning

confidence: 99%

“…Since it is an open loop control, it is not robust when disturbances act on the system. In [5] we have proposed a closed loop control approach where the control objective is expressed as a reference model. The controller design is based on the residuation theory applied to particular mappings.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control for (max,+)-linear Systems in the Presence of Disturbances

2004

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Section: Output Feedbackmentioning

confidence: 99%

Section: Output Feedbackmentioning

confidence: 99%

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Optimal Control for (max,+)-linear Systems in the Presence of Disturbances

2004

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“…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. In Maia et al (2003) an optimal controller is derived based on residuation theory that guarantees also stability.…”

Section: Introductionmentioning

confidence: 99%

“…However, the residuation-based approach does not cope with input and state constraints. Moreover, the methods presented in Menguy et al (1997) and Cottenceau et al (2001) cannot solve tracking problems corresponding to the case when the actual outputs do not necessarily have to occur before the due dates although these situations are often met in many practical applications. Some of these drawbacks are removed in Maia et al (2003), Menguy et al (2000), and Necoara (2006) by using respectively projection, an adaptive approach, or MPC.…”

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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Robust control of constrained max‐plus‐linear systems

Necoara

Schutter

Boom

et al. 2008

Intl J Robust & Nonlinear

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Max-plus-linear (MPL) systems are a class of nonlinear systems that can be described by models that are 'linear' in the max-plus algebra. We provide here solutions to the three types of finite-horizon min-max control problems for uncertain MPL systems, depending on the nature of the control input over which we optimize: open-loop input sequences, disturbances feedback policies, and state feedback policies. We assume that the uncertainty lies in a bounded polytope and that the closed-loop input and state sequence should satisfy a given set of linear inequality constraints for all admissible disturbance realizations. Despite the fact that the controlled system is nonlinear, we provide sufficient conditions that allow one to preserve convexity of the optimal value function and its domain. As a consequence, the min-max control problems can be either recast as a linear program or solved via N parametric linear programs, where N is the prediction horizon. In some particular cases of the uncertainty description (e.g. interval matrices), by employing results from dynamic programming, we show that a min-max control problem can be recast as a deterministic optimal control problem.

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Model reference control for timed event graphs in dioids

Cited by 103 publications

References 6 publications

Optimal Control for (max,+)-linear Systems in the Presence of Disturbances

Optimal Control for (max,+)-linear Systems in the Presence of Disturbances

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

Robust control of constrained max‐plus‐linear systems

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