Constrained regulation of continuous Petri nets |
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| Authors: | Redouane Kara Mourad Ahmane Jean Jacques Loiseau Said Djennoune |
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| Institution: | aInstitut de Recherche en Communications et Cybernétique de Nantes, UMR-CNRS 6597, 1 rue de la Noë, 44321 Nantes cedex 03, France;bLaboratoire de Conception et Conduite des Systèmes de Production, route de Hasnaoua BP 17, Université Mouloud Mammeri de Tizi-Ouzou, 15000, Algérie;cLaboratoire Systèmes et Transport (SET-EA 3317), Université de Technologie de Belfort-Montbéliard, 90010 Belfort Cedex, France |
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| Abstract: | This paper deals with constrained regulation of continuous Petri nets under the so-called infinite servers semantics. Our aim is to design feedback gains that permit us to reach both desired stationary marking vector and desired asymptotic firing rate vector. The proposed approach takes into account constraints on the control, the marking of the Petri net, and the stability of the closed-loop system. The existence of a solution is first expressed geometrically, in terms of the inclusion of two polyhedral sets. They are reformulated algebraically as linear matrix inequalities, which provides an effective way to calculate feedback gains answering the problem. Finally, an application to an assembly production system is given. |
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| Keywords: | Discrete event systems Continuous Petri net Positive invariance Contractivity Polyhedral sets Linear Matrix Inequalities (LMI) |
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