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 Fr ́echet subdifferentials of V along optimal trajectories. Then, we extend the analysis to the sub- and 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 C2 regularity of V on neighborhoods of optimal trajectories.

Cannarsa, P., Frankowska, H., & Scarinci, T. (2015). Second-order sensitivity relations and regularity of the value function for Mayer's problem in optimal control. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 53(6), 3642-3672 [10.1137/14098346X].

Second-order sensitivity relations and regularity of the value function for Mayer's problem in optimal control

CANNARSA, PIERMARCO;SCARINCI, TERESA
2015

Abstract

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 Fr ́echet subdifferentials of V along optimal trajectories. Then, we extend the analysis to the sub- and 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 C2 regularity of V on neighborhoods of optimal trajectories.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
Mayer problem; differential inclusion; maximum principle; sensitivity relations; Riccati equation
Cannarsa, P., Frankowska, H., & Scarinci, T. (2015). Second-order sensitivity relations and regularity of the value function for Mayer's problem in optimal control. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 53(6), 3642-3672 [10.1137/14098346X].
Cannarsa, P; Frankowska, H; Scarinci, T
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/170471
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