Controllability and optimal control of the transport equation with a localized vector field
| Autor: | Michel Duprez, Francesco Rossi, Morgan Morancey |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Marseille (I2M), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), Laboratoire des Sciences de l'Information et des Systèmes (LSIS), Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Paristech ENSAM Aix-en-Provence-Université de Toulon (UTLN)-Aix Marseille Université (AMU), Univ Malta, ANR-16-CE33-0008,CroCo,Commande de foules : de la théorie du contrôle aux applications au trafic routier(2016), ANR-11-IDEX-0001,Amidex,INITIATIVE D'EXCELLENCE AIX MARSEILLE UNIVERSITE(2011), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Arts et Métiers Paristech ENSAM Aix-en-Provence-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
Class (set theory) Control and Optimization 02 engineering and technology Type (model theory) Distributed systems 01 natural sciences 020901 industrial engineering & automation Mathematics - Analysis of PDEs Control theory [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Optimisation 0101 mathematics Mathematics - Optimization and Control Mathematics Agents and agent-based systems Partial differential equation Lipschitz continuity Optimal control Modeling and Simulation 010101 applied mathematics Controllability Optimization and Control (math.OC) Vector field [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Convection–diffusion equation Analysis of PDEs (math.AP) |
| Zdroj: | Mediterranean Conference on Control and Automation 25th Mediterranean Conference on Control and Automation (MED) 25th Mediterranean Conference on Control and Automation (MED), Univ Malta, Jul 2017, Valletta, Malta. pp.74-79, ⟨10.1109/MED.2017.7984098⟩ MED |
| DOI: | 10.1109/MED.2017.7984098⟩ |
| Popis: | International audience; We study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling such system with a control being a Lipschitz vector field on a fixed control set ω. We prove that, for each initial and final configuration, one can steer one to another with such class of controls only if the uncontrolled dynamics allows to cross the control set ω. We also prove a minimal time result for such systems. We show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in ω to feed the desired final configuration. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|