On the local controllability for optimal control problems

A. V. Arutyunov, S. E. Zhukovskiy

We consider an optimal control problem on the fixed interval of time with the right endpoint constraint. We introduce the concept of controllability for this problem. The main result of the paper states that if for the optimal control problem the Pontryagin maximum principle fails on the given admissible process then this process satisfies the controllability condition.