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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.
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.
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