State-constrained stochastic optimal control problems via reachability approach
| Autor: | Hasnaa Zidani, Athena Picarelli, Olivier Bokanowski |
|---|---|
| Přispěvatelé: | Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Mathematical Institute [Oxford] (MI), University of Oxford [Oxford], Optimisation et commande (OC), Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Programme Gaspard Monge pour l'Optimisation, ANR-11-IDEX-0003,IPS,Idex Paris-Saclay(2011), European Project: 264735,EC:FP7:PEOPLE,FP7-PEOPLE-2010-ITN,SADCO(2011), University of Oxford |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization State variable Control and Optimization stochastic target problems Control variable Boundary (topology) 02 engineering and technology 01 natural sciences 020901 industrial engineering & automation Reachability Bellman equation [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Hamilton-Jacobi equations state constraints stochastic optimal control viscosity notion 0101 mathematics [MATH]Mathematics [math] Mathematics Stochastic control Epigraph 49L25 Applied Mathematics 93E20 010101 applied mathematics Controllability stochastic target problems AMS subject classifications: 49L20 state-constraints 35K55 [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
| Zdroj: | SIAM Journal on Control and Optimization SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, 54 (5), pp.2568-2593. ⟨10.1137/15M1023737⟩ SIAM Journal on Control and Optimization, 2016, 54 (5), pp.2568-2593. ⟨10.1137/15M1023737⟩ |
| ISSN: | 0363-0129 1095-7138 |
| DOI: | 10.1137/15M1023737⟩ |
| Popis: | International audience; This paper deals with a class of stochastic optimal control problems (SOCP) in presence of state-constraints. It is well-known that for such problems the value function is, in general, discontinuous and its characterization by a Hamilton-Jacobi equation requires additional assumptions involving an interplay between the boundary of the set of constraints and the dynamics of the controlled system. Here, we give a characterization of the epigraph of the value function without assuming the usual controllability assumptions. For this end, the SOCP is first translated into a state-constrained stochastic target problem. Then a level-set approach is used to describe the backward reachable sets of the new target problem. It turns out that these backward-reachable sets describe the value function. The main advantage of our approach is that it allows to handle easily the state constraints by an exact penalization. However, the target problem involves a new state variable and a new control variable that is unbounded. |
| Databáze: | OpenAIRE |
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