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A conditional gradient method for a class of time-lag optimal control problems

Published online by Cambridge University Press:  17 February 2009

K. H. Wong  and
K. L. Teo
K. L. Teo
Affiliation:
School of Mathematics, University of New South Wales, P.O. Box 1, Kensington, N.S.W. 2033.
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Abstract

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In this paper, we consider a class of optimal control problems with discrete time delayed arguments and bounded control region. A computational algorithm for solving this class of time lag optimal control problems is developed by means of the conditional gradient technique. The convergence property of the algorithm is also investigated.

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 4 , April 1984 , pp. 518 - 537
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Ahmed, N. U., “Existence of optimal controls for a class of hereditary systems with lagging control”, J. Inform. Control 26 (1974), 178–185.CrossRefGoogle Scholar
[2]Banks, H. T., “Necessary conditions for control problems with variable time lags”, SIAM J. Control 6 (1968), 9–47.CrossRefGoogle Scholar
[3]Banks, H. T. and Burns, J. A., “Hereditary control problems: numerical methods based on averaging approximations”, SIAM J. Control Optim. 6 (1978), 169–208.CrossRefGoogle Scholar
[4]Blatt, J. M., “Control systems with time delays”, J. Austral. Math. Soc. Ser. B 19 (1976), 478–492.CrossRefGoogle Scholar
[5]Friedman, A., “Optimal control for hereditary processes”, Arch. Rational Mech. Anal. 15 (1964), 396–416.CrossRefGoogle Scholar
[6]Georganas, N. D., “Optimal control for a class of hereditary systems”, Ph. D. Thesis, University of Ottawa, Ottawa, Canada, 1970.Google Scholar
[7]Georganas, N. D., “Optimization in a class of hereditary systems with direct penalization of the initial data”, Internat. J. Systems Sci. 5 (1974), 295–299.CrossRefGoogle Scholar
[8]Georganas, N. D. and Ahmed, N. U., ”, J. Inform. Control 22 (1973), 394–402.CrossRefGoogle Scholar
[9]Halanay, G., “Optimal controls for systems with time-lag”, SIAM J. Control 6 (1968), 215–235.CrossRefGoogle Scholar
[10]Himmelberg, C. J., Jacobs, M. Q. and Van Vleck, F. S., “Measurable multi-functions, selectors, and Filippov's implicit functions lemma”, J. Math. Anal. Appl. 25 (1969), 276–284.CrossRefGoogle Scholar
[11]Lee, E. B., “Variational problems for systems having delay in the control action”, IEEE Trans. Automat. Control 13 (1969), 697–699.CrossRefGoogle Scholar
[12]Mayne, D. Q. and Polak, E., “First-order strong variation algorithms for optimal control”, J. Optim. Theory Appl. 16 (1975), 303–325.CrossRefGoogle Scholar
[13]Murray, J. M. and Teo, K. L., “On a computational algorithm for a class of optimal control problems involving discrete time delayed arguments”, J. Austral. Math. Soc. Ser. B 20 (1978), 315–343.CrossRefGoogle Scholar
[14]Oguztoreli, M. N., Time-lag control systems (Academic Press, New York, 1966).Google Scholar
[15]Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V. and Mischenko, E. F., The mathematical theory of optimal processes (John Wiley and Sons (Interscience Publishers), New York, 1962), 213–226.Google Scholar
[16]Teo, K. L. and Craven, B. D., “On a computational algorithm for time-lag optimal control problems with restricted phase coordinates”, J. Austral. Math. Soc. Ser. B 21 (1980), 385–397.CrossRefGoogle Scholar
[17]Teo, K. L. and Moore, E. J., “Necessary conditions for optimality for control problems with time delays appearing in both state and control variables”, J. Optim. Theory Appl. 23 (1977), 413–428.CrossRefGoogle Scholar
[18]Teo, K. L., Wu, Z. S. and Clements, D. J., “A computational method for convex optimal control problems involving linear hereditary system”, Internat. J. System Sci. 12 (1981), 1045–1060.CrossRefGoogle Scholar