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RESEARCH PAPERS

On a Problem of Letov in Optimal Control

[+] Author and Article Information
C. D. Johnson

Electrical Engineering Department, University of Alabama, Huntsville Center, Huntsville, Ala.

W. M. Wonham

Center for Control Theory, RIAS, Baltimore, Md.

J. Basic Eng 87(1), 81-89 (Mar 01, 1965) (9 pages) doi:10.1115/1.3650531 History: Received March 23, 1964; Online November 03, 2011

Abstract

In a series of papers [1, 2], A. M. Letov discussed an optimal regulator problem for a linear plant with bounded control variable and quadratic performance index. This problem was also discussed by Chang [3]. Krasovskii and Letov observed later [4] that the solution proposed in [1, 2, and 3] may be correct only for special choices of the initial value of the state vector. In the present note, further aspects of the solution in the general case are described and three examples are given. The possible existence of a regime of unsaturated-nonlinear optimal control is demonstrated. The presence of this regime in the optimal control law was apparently overlooked in [1–4].

Copyright © 1965 by ASME
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