An approach to sub-optimal feedback control of non-linear systems

W. L. Garrard, N. H. McClamroch, L. G. Clark

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51 Scopus citations


A method is developed for the determination of sub-optimal control laws for non-linear dynamical systems. The control laws determined by the use of this method are in time invariant, feedback form and approximately minimize a performance index which is the integral of a positive definite function of the state plus a quadratic function of the control. The basis of the proposed technique is a method for the determination of approximate solutions for the associated Hamilton-Jacobi-Bellman equation. The method is applied to two examples and the results are shown to compare favourably with those obtained by use of other sub-optimal control procedures. The method developed in this paper is applicable, in a practical sense, to systems of higher than second order and seems to hold promise as a means for solving a large class of optimization problems.

Original languageEnglish (US)
Pages (from-to)425-435
Number of pages11
JournalInternational Journal of Control
Issue number5
StatePublished - May 1967
Externally publishedYes

Bibliographical note

Funding Information:
ACKHOWLEUGBIENT This work was supported in part by NASA Grant NAS 5-15120.


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