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

[+] Author and Article Information
Yu-Chi Ho

Division of Engineering and Applied Physics, Harvard University, Cambridge, Mass.; Minneapolis Honeywell Regulator Company, Boston, Mass.

J. Basic Eng 84(1), 33-37 (Mar 01, 1962) (5 pages) doi:10.1115/1.3657263 History: Received March 01, 1961; Online November 04, 2011


A class of problems that has received considerable attention in recent years from both control theorists and engineers is the following:

Given  = 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  = 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.

Copyright © 1962 by ASME
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