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Regularity along optimaltrajectories of the value function of a Mayer problem

Published online by Cambridge University Press:  15 October 2004

Carlo Sinestrari
Carlo Sinestrari*
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica 1, 00133 Roma, Italy; sinestra@mat.uniroma2.it.
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Abstract

We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.

Keywords

Optimal controlvalue functionsemiconcavity.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 4 , October 2004 , pp. 666 - 676
Copyright
© EDP Sciences, SMAI, 2004

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