Automatic Controls for Nonlinear Dynamical Systems with Lipschitzian Trajectories

Abstract

We would like to investigate on the solution to the automatic control problem given by the differential equation y′(t)=f(t,y(t),w(t)) for a given initial function x in the initial domain D(x,ω,Y) for almost all t in the interval I, with controls given by w(t)=g(t,y(t),T(y)(t)), where T is a nonanticipating and Lipschitzian operator. The result will be generalized for a dynamical system y′(t)=f(t,y(t),T(y),u(t)).