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A maximum principle for optimal control for a class of controlled systems

Published online by Cambridge University Press:  17 February 2009

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Abstract

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Applying Ekeland's variational principle in this paper, we obtain a maximum principle for optimal control for a class of two-point boundary value controlled systems. The control domain need not be convex. For a special case, that is the so called LQ-type problem, we obtain the optimal control in the closed loop form and a corresponding Riccati type differential equation.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Ahmed, N. U., “Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space”, J. Optim. Theory Appl. 50 (1986) 213237.CrossRefGoogle Scholar
[2]Ahmed, N. U., Elements of finite-dimensional systems and control theory (Longman, England, 1988).Google Scholar
[3]Ekeland, I., “On the variational principle”, J. Math. Anal. and Applic. 47 (1974) 324353.CrossRefGoogle Scholar
[4]Pontryagin, L. S. et al. , The Mathematical Theory of Optimal Processes (Wiley, New York, 1962).Google Scholar
[5]Rehbock, V., Teo, K. L. and Jennings, L. S., “A computational procedure for suboptimal robust controls”, Dynamics and Control 2 (1992) 331348.CrossRefGoogle Scholar
[6]Teo, K. L., Goh, C. J. and Wong, K. H., A unified computational approach to optimal control problems (Longman, England, 1991).Google Scholar
[7]Wang, R. and Wu, Z., Ordinary differential equations, in Chinese, (Advanced Educational Publishing Company, Peking, 1987).Google Scholar