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On the dynamic programming approach to Pontriagin's maximum principle

Published online by Cambridge University Press:  14 July 2016

Richard Morton
Richard Morton*
Affiliation:
University of Manchester
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Extract

Suppose that the state variables x = (x1,…,xn)′ where the dot refers to derivatives with respect to time t, and u ∊ U is a vector of controls. The object is to transfer x to x1 by choosing the controls so that the functional takes on its minimum value J(x) called the Bellman function (although we shall define it in a different way). The Dynamic Programming Principle leads to the maximisation with respect to u of and equality is obtained upon maximisation.

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 3 , December 1968 , pp. 679 - 692
Copyright
Copyright © Applied Probability Trust 1968 

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References

[1] Pontriagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., and Mishchemko, E. F. (1962) The Mathematical Theory of Optimal Processes. (Trans. Trirogoff, .) Wiley and Sons, N. Y. Google Scholar
[2] Athans, M. and Falb, P. L. (1966) Optimal Control. McGraw-Hill, N. Y. Google Scholar
[3] Desoer, C. A. (1961) Pontriagin's maximum principle and the principle of optimality. J. Franklin Inst. 271, 361–367. Addendum (1962) J. Franklin Inst. 272, 313.Google Scholar
[4] Boltyanskii, V. G. (1966) Sufficient conditions for optimality and the justification of the dynamic programming method. SIAM J. Control. 4, 326–361.Google Scholar
[5] Bellman, R. (1962) Dynamic Programming. Princeton Univ. Press.Google Scholar