Аннотация:We consider an optimal control problem with a mixed functional and free stopping time. Dynamics of the system is given by means of a differential inclusion. The integral term of the functional contains the characteristic function of a given open set M⊂Rn which can be interpreted as a “risk” or “dangerous” zone. The statement of the problem can be treated as a weakening of the statement of the classical optimal control problem with state constraints. We study relationships between these two problems. An illustrative example is presented as well.