On a nonlinear problem of a sequential control with a parameter

The problem of evasion of a group of moving points from a nonlinear controlled object, whose goal is consecutively approach these points in a prescribed order, is analyzed. The movement of each point is defined uniquely by a scalar parameter chosen at the initial time instant. The controlled object minimizes a certain cost function, and the group of the points, acting cooperatively, maximize this cost function by choosing the parameters. Necessary optimality conditions for parameters are obtained. A model problem of an evasion of moving points from a vehicle is solved.