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Optimal control problems with elastic collisions

Published online by Cambridge University Press:  17 February 2009

J. M. Murray
J. M. Murray
Affiliation:
School of Mathematics, University of N.S.W., Box 1, Kensington, N.S.W., 2033, Australia.
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Abstract

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In this paper consider we optimal control problems with linear state constraints where the states can be discontinuous at the boundary. In fact the state vector models the cause the position and velocity of a particle where the collisions with the boundary that cause the discontinuities are elastic. Necessary conditions are derived by looking at limits of approximate problems that are unconstrained.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 4 , April 1989 , pp. 470 - 482
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Berkovitz, L. D., Optimal control theory (Springer-Verlag, New York, 1974).CrossRefGoogle Scholar
[2]Clark, C. W., Clarke, F. H. and Munro, G. R., “The optimal exploitation of renewable resource stocks”, Econometrica 47 (1979) 25–47.CrossRefGoogle Scholar
[3]larke, F. H., Optimization and nonsmooth analysis (Wiley, New York, 1983).Google Scholar
[4]Graves, L. M., The theory of functions of real variables (McGraw-Hill, New York, 1946).Google Scholar
[5]Hille, E., Lectures on ordinary differential equations (Addison-Wesley, 1969).Google Scholar
[6]Levine, W. S. and Zajac, F. E., “An example of optimal control of a system with discontinuous state”, in Analysis and optimization of systems (eds. Bensoussan, A. and Lions, J. L.), (1984) 534–541.Google Scholar
[7]Neustadt, L. W., “A general theory of minimum-fuel space trajectories”, SIAM J. Con. Opt. 3 (1965) 317–356.Google Scholar