Second-order sensitivity relations and regularity of the value function for Mayer's problem in optimal control
| Autor: | Piermarco Cannarsa, Hélène Frankowska, Teresa Scarinci |
|---|---|
| Přispěvatelé: | Scarinci, Teresa, Sensitivity Analysis for Deterministic Controller Design - SADCO - - EC:FP7:PEOPLE2011-01-01 - 2014-12-31 - 264735 - VALID, Dipartimento di Matematica [Roma II] (DIPMAT), Università degli Studi di Roma Tor Vergata [Roma], Institut de Mathématiques de Jussieu (IMJ), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), 'Instituto Nazionale di Alta Matematica' (INdAM), through the GNAMPA Research Project 2014, European Project: 264735,EC:FP7:PEOPLE,FP7-PEOPLE-2010-ITN,SADCO(2011) |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
0209 industrial biotechnology
Control and Optimization 34A60 49J53 02 engineering and technology 01 natural sciences sensitivity relations Riccati equation 020901 industrial engineering & automation Maximum principle Differential inclusion Settore MAT/05 - Analisi Matematica Bellman equation Mayer problem differential inclusion maximum principle FOS: Mathematics Sensitivity relations Sensitivity (control systems) Differentiable function 0101 mathematics Mathematics - Optimization and Control Mathematics Applied Mathematics 010102 general mathematics Conjugate points Mathematical analysis [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC] Optimal control Optimization and Control (math.OC) [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, 2015, 53 (6), pp 3642/3672 SIAM Journal on Control and Optimization, 2015, 53 (6), pp 3642/3672 |
| ISSN: | 0363-0129 1095-7138 |
| Popis: | 29 pages; International audience; This paper investigates the value function, $V$, of a Mayer optimal control problem with the state equation given by a differential inclusion. First, we obtain an invariance property for the proximal and Fréchet subdifferentials of $V$ along optimal trajectories. Then, we extend the analysis to the sub/superjets of $V$, obtaining new sensitivity relations of second order. By applying sensitivity analysis to exclude the presence of conjugate points, we deduce that the value function is twice differentiable along any optimal trajectory starting at a point at which $V$ is proximally subdifferentiable. We also provide sufficient conditions for the local $C^2$ regularity of $V$ on tubular neighborhoods of optimal trajectories. |
| Databáze: | OpenAIRE |
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