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

Abstract

A class of problems that has received considerable attention in recent years from both control theorists and engineers is the following: Given ẋ = Fx + du, x(0) = cDetermine |u(t)| ≤ 1 such that x(T) = 0 and x(t) ≠ 0for 0 ≤ t < T and where T is a minimum (P-1) A related and perhaps more practical class of problems can be stated as Given ẋ = Fx + du, x(0) = cDetermine |u(t)| ≤ 1 such that ‖x(T)‖2P is a minimum for given T (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.