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

The hysteresis phenomenon arises in many branches of science and engineering. The problems with hysteresis are essentially nonlinear. The mathematical model of hysteresis models the after-effect process. The survey is devoted to the optimal control problem with hysteresis nonlinear characteristics. It is required to determine the minimum of goal function under some constraints when terminal moment can be free or fixed. In general nonlinear case the solution is searched in the class of generalized controls. In important special case the control problem can be reduced to linear concave optimization problem. The main goal is to formulate and to prove necessary conditions for first-order optimality. The derivation of necessary conditions is based on traditional approach in accordance with which the optimal control problem is formulated as the optimization problem and necessary conditions is derived by generalized Lagrange method of multipliers.