Regularity along optimal trajectories of the value function of a Mayer problem
ESAIM: Control, Optimisation and Calculus of Variations, Volume 10 (2004) no. 4, p. 666-676

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.

DOI : https://doi.org/10.1051/cocv:2004026
Classification:  49L20,  49K15
Keywords: optimal control, value function, semiconcavity
@article{COCV_2004__10_4_666_0,
     author = {Sinestrari, Carlo},
     title = {Regularity along optimal trajectories of the value function of a Mayer problem},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {10},
     number = {4},
     year = {2004},
     pages = {666-676},
     doi = {10.1051/cocv:2004026},
     zbl = {1068.49028},
     mrnumber = {2111087},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2004__10_4_666_0}
}
Sinestrari, Carlo. Regularity along optimal trajectories of the value function of a Mayer problem. ESAIM: Control, Optimisation and Calculus of Variations, Volume 10 (2004) no. 4, pp. 666-676. doi : 10.1051/cocv:2004026. http://www.numdam.org/item/COCV_2004__10_4_666_0/

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