Bond graph formulation of an optimal control problem for linear time invariant systems
| Autor: | Daniel Thomasset, Jérôme Pousin, Bogdan Chereji, Martine Picq, Wilfrid Marquis-Favre, Omar Mouhib |
|---|---|
| Přispěvatelé: | Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2008 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization Optimization problem Computer Networks and Communications Applied Mathematics 02 engineering and technology bond graph Optimal control [SPI.AUTO]Engineering Sciences [physics]/Automatic Dynamic programming LTI system theory 020303 mechanical engineering & transports 020901 industrial engineering & automation Graph bandwidth 0203 mechanical engineering Control and Systems Engineering Signal Processing Closure problem bicausality Pontryagin Maximum Principle Bond graph port-Hamiltonian system Mathematics Moral graph |
| Zdroj: | Journal of The Franklin Institute Journal of The Franklin Institute, Elsevier, 2008, 345 (4), pp.349-373. ⟨10.1016/j.jfranklin.2007.10.005⟩ |
| ISSN: | 0016-0032 |
| Popis: | Post-print version.; International audience; A recent communication has proposed a conjectural procedure for representing a category of optimal control problems in bond graph language [W. Marquis-Favre, B. Chereji, D. Thomasset, S. Scavarda, Bond graph representation of an optimal control problem: the dc motor example, in: ICBGM' 05 International Conference of Bond Graph Modelling and Simulation, New Orleans, USA, January 23-27, 2005, pp. 239-244]. This paper aims at providing a fundamental theory for proving the effectiveness of this procedure. The class of problem that the procedure can deal with has been extended. Its application was formerly restricted to linear time invariant SISO system. The systems considered now are linear time invariant MIMO systems. The optimization objective is the minimization of dissipation and input. The developments concerning the optimal control problem are based on the Pontryagin maximum principle and the proof of the effectiveness of the procedure makes a broad use of the port-Hamiltonian concept. As a result, the bond graph representation of the given optimization problem enables the analytical system, which provides the optimal solution, to be derived. The work presented in this paper is the first step in research with perspectives towards formulating dynamic optimization problems in bond graph and, towards coupling this formulation with a sizing methodology using bond graph language and a state-space inverse model approach. This sizing methodology, however, is not the topic of this paper and thus is not presented here. |
| Databáze: | OpenAIRE |
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