Properties of the Bellman function in time-optimal control problems
The author considers a nonautonomous, nonlinear time-optimal control problem and addresses the question of Hölder and Lipschitz continuity of the optimal value function. Under usual regularity conditions, and for arbitrary closed targets a condition on a lower Dini derivative at the boundary of the target is established which guarantees Hölder continuity of the solution, allowing also an estimate for the Hölder coefficient. This condition is then modified using the exterior normal cone at each boundary point of the target. The modified condition derived this way is shown to be equivalent to the Lipschitz continuity of the value function.
scientific article; zbMATH DE number 1069776
scientific article