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Control systems with time lags

Published online by Cambridge University Press:  17 February 2009

John M. Blatt
Affiliation:
Department of Applied Mathematics, University of New South Wales, Kensington, Australia.
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Abstract

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Necessary conditions for optimal controls are given for non-linear systems with time delayed effects in both control and state variables.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Pontryagin, L. S., Boltyanskii, V. O., Gramkrelidze, R. V. and Mishchenko, E. F., The Mathematical Theory of Optimal Processes, New York: Interscience Publishers, Inc., (1962); in particular, see pages 213 ff.Google Scholar
[2]Friedman, Avner, ‘Optimal Control for Hereditary Processes’, Arch. Rational Mech. Anal. 15 (1964), 396.CrossRefGoogle Scholar
[3]Oguztoreli, M. N., Time-Lag Control Systems, New York: Academic Press, (1966).Google Scholar
[4]Banks, H. T., ‘Necessary Conditions for Control Problems with Variable Time Lags’, SIAM J. Control 6 (1968), 947.CrossRefGoogle Scholar
[5]Kharatishvili, G. L., ‘A Maximum Principle in Extremal Problems with Delays’, Proc. Conf. on Math. Theory of Control, Univ. of South. Calif. edited by Balakrishnan, A. V. and Neustadt, L. W., New York: Academic Press (1967), 2634.Google Scholar
[6]Halanay, A., ‘Optimal Controls for Systems with Time-Lag’, SIAM J. Control 6 (1968), 215235.CrossRefGoogle Scholar
[7]Lee, E. B., ‘Variational Problems for Systems having Delay in the Control Action, I.E.E.E. Trans. on Aut. Control (1968), 697699.Google Scholar
[8]Lee, E. B. and Markus, L., Foundations of Optimal Control Theory, New York: John Wiley (1967).Google Scholar
[9]Day, K. S. and Hsia, T. C., ‘Optimal Control of Linear Time-Lag Systems’, Proc. J.A.C.C., The University of Michigan (1968), 10461055.Google Scholar
[10]Chyung, D. H. and Lee, E. B., Optimal Systems with Time Delays, Proc. 3rd I.F.A.C. Conf., London (1966).Google Scholar
[11]Georganas, N. D., Optimal Control for a Class of Hereditary Systems, Ph.D. thesis, Dept. of Elec. Eng., University of Ottawa (1970).Google Scholar
[12]Georganas, N. D., “Optimization in a class of hereditary systems with direct penalization of the initial data”, Int. J. Systems Sci. 5 (1974), 295299.CrossRefGoogle Scholar
[13]Hadley, G. and Kemp, M. C., Variational Methods in Economics, Amsterdam: North- Holland Publishing Coy. (1971).Google Scholar
[14]Teo, K. L. and Moore, E. J., ‘Necessary Conditions for Optimality for Control Problems with Time Delays Appearing in Both State and Control Variables’, to be published.Google Scholar