One minimization problem connected with spread of trajectories of controlled object

It is considered one minmax control problem for quasilinear controlled object. There are two sorts of controls in considered object. One of them models variable perturbation of influences which act on controlled object. The second of them is constant control vector. It is used for compensation of perturbation factors. This control is restricted by given set. The equality of control couple is rated with the help of some continuous function. This function is defined on the phase space. It was studied the maximum of this function on attainable set of our control object under consideration. The attainable set characterizes spread of trajectories for our control object in fixed time. This maximum depends on constant control vector from given set. We want minimize this marginal function on the set of constant controls. In paper it are studied properties of this marginal function. It is proved the existence of its minimum on the set of constant vector controls. Also for some sufficient conditions it was proved that considered marginal function has Lipschitz property.