Optimal control for systems described by ordinary differential equations with nonlinear characteristics of hysteresis type

The paper presents the continuation of the survey of optimal control problems with hysteresis nonlinear characteristics which has been begun in previous issue. It is required to determine the minimum of goal function under some constraints when terminal time can be free or fixed. In general case the solution is searched in the class of generalized controls. The author shows that the conjugate variables in maximum principle are uniformly bounded. The limiting transition in conjugate equation is considered. The maximum principle is used for the problem of quick-action for the systems with hysteresis. In nondifferentiable case the initial optimal control problem is approximated by the family of differentiable problems and necessary conditions of optimality are obtained by limiting transition.