On a Successive Approximation Technique in Solving Some Control System Optimization Problems

[+] Author and Article Information
Masanao Aoki

Department of Engineering, University of California, Los Angeles, Calif.

J. Basic Eng 85(2), 177-180 (Jun 01, 1963) (4 pages) doi:10.1115/1.3656555 History: Received April 20, 1962; Online November 03, 2011


It has been realized for some time that most realistic optimization problems defy analytical solutions in closed forms and that in most cases it is necessary to resort to judicious combinations of analytical and computational procedures to solve problems. For example, in many optimization problems, one is interested in obtaining structural information on optimal and “good” suboptimal policies. Very often, various analytical as well as computational approximation techniques need be employed to obtain clear understandings of structures of policy spaces. The paper discusses a successive approximation technique to construct minimizing sequences for functionals in extremal problems, and the techniques will be applied, to a class of control optimization problems given by:

Minv   J(v) = Minv   01 g(u. v)dt,
where du/dt = h(u, v), h(u, v) linear in u and v, and where u and v are, in general, elements of Banach spaces. In Section 2, the minimizing sequences are constructed by approximating g(u, v) by appropriate quadratic expressions with linear constraining differential equations. It is shown that under the stated conditions the functional values converge to the minimal value monotonically. In Section 3, an example is included to illustrate some of the techniques discussed in the paper.

Copyright © 1963 by ASME
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