Regularity along optimal trajectories of the value function of a Mayer problem
Dipartimento di Matematica, Università di Roma
“Tor Vergata”, via della Ricerca Scientifica 1, 00133 Roma, Italy; email@example.com.
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.
Mathematics Subject Classification: 49L20 / 49K15
Key words: Optimal control / value function / semiconcavity.
© EDP Sciences, SMAI, 2004