A nonlinear optimal control in inverse problem for a system with parabolic equation

It is studied the questions of solvability of the nonlinear dot mobile point problem of nonlinear optimal control in inverse problem for a system with parabolic and ordinary differential equations in the case of presence of several dot mobile sources. Parabolic equation is considered with mixed value and nonlocal integral conditions, while ordinary differential equation is considered with initial value condition. It is formulated the necessary conditions for nonlinear optimal control. Determination of the optimal control function is reduced to the complex functional-integral equation, the solving process of which is composed of solutions of two different equations: nonlinear functional equations and nonlinear integral equations. It is obtained the formulas for approximation calculating the state function, restore function and dot mobile nonlinear optimal control and the estimate for the permissible error with respect to optimal control.