A Successive Approximation Technique for Optimal Control Systems Subject to Input Saturation

A class of problems that has received considerable attention in recent years from both control theorists and engineers is the following: Givenx˙=Fx+du,x(0)=cDetermine|u(t)|≤1suchthatx(T)=0andx(t)≠0for0≤t<TandwhereTisaminimum(P-1) A related and perhaps more practical class of problems can be stated as Givenx˙=Fx+du,x(0)=cDetermine|u(t)|≤1suchthat‖x(T)‖2PisaminimumforgivenT(P-2) Although a considerable amount of effort has been expended on (P-1), and to a lesser extent on (P-2), yet computational techniques which enable one to solve numerically the above problems are still lacking except in restricted cases [7, 8]. This paper presents such a technique which completely solves this problem by successive approximation. The convergence of this solution is proved, and it is shown to satisfy all known properties of the problems.