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Optimal control theory with general constraints

Published online by Cambridge University Press:  17 February 2009

John M. Blatt
John M. Blatt
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033
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Abstract

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We consider an optimal control problem with, possibly time-dependent, constraints on state and control variables, jointly. Using only elementary methods, we derive a sufficient condition for optimality. Although phrased in terms reminiscent of the necessary condition of Pontryagin, the sufficient condition is logically independent, as can be shown by a simple example.

Type
Research Article
Information
The ANZIAM Journal , Volume 23 , Issue 2 , October 1981 , pp. 115 - 126
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Asher, R. B. and Sebesta, H. R., “Optimal control of systems with state-dependent time delay”, Int. J. of Control 14 (1971), 353–365.CrossRefGoogle Scholar
[2]Bell, D. J. and Jacobson, D. H., Singular, optimal control problems (Academic Press, New York, 1975).Google Scholar
[3]Hadley, G. and Kemp, M. C., Variational methods in economics (North Holland, Amsterdam, 1971).Google Scholar
[4]Hestenes, M. R., Calculus of variations and optimal control theory (Wiley, New York, 1966).Google Scholar
[5]Van Long, Ngo and Vousden, Neil, “Optimal control theorems”, Essay 1 in Pitchford, J. D. and Turnovsky, S. J. (editors), Applications of control theory to economic analysis (North Holland, Amsterdam, 1977).Google Scholar
[6]Mangasarian, O. L., “Sufficient conditions for the optimal control of nonlinear systems”, J. SIAM Control 4 (1966), 139–152.CrossRefGoogle Scholar
[7]Neustadt, Lucien W., Optimization–A theory of necessary conditions (Princeton University Press, Princeton, 1976).Google Scholar
[8]Pontryagin, L. S., Boltyanskii, V. G., Gamkreidze, R. V., and Mishchenko, E. F., The mathematical theory of optimal process (John Wiley, New York, 1962).Google Scholar
[9]Schwarzkopf, A. B., “Optimal controls with equality state constraints”, J. Optim. Theor. Appl. 19 (1976), 455–468.CrossRefGoogle Scholar
[10]Sebesta, H. R. and Clark, L. G., “On the optimal-control problem for dynamical processes with variable delays”, Trans. A.S.M.E., J. of Basic Engineering 90 (1968), 181–194.CrossRefGoogle Scholar
[11]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. B 21 (1980), 385–397.CrossRefGoogle Scholar