Automatic Controls for Nonlinear Dynamical Systems with Lipschitzian Trajectories

We would like to investigate on the solution to the automatic control problem given by the differential equation y Žt. fŽt, yŽt.,wŽt.. for a given initial function x in the initial domain DŽx, , Y.for almost all t in the interval I, with controls given by wŽt. gŽt, yŽt.,TŽy.Žt.., where T is a nonanticipating and Lipschitzian operator. The result will be generalized for a dynamical system y Žt. fŽt, yŽt., TŽy., uŽt...