Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T06:45:29.227Z Has data issue: false hasContentIssue false
  • English
  • Français

An optimal control problem in exterior hydrodynamics

Published online by Cambridge University Press:  14 November 2011

S. S. Sritharan
S. S. Sritharan
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, U.S.A
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper we consider the problem of accelerating an obstacle in an incompressible viscous fluid from rest to a given speed in a given time with minimum energy expenditure. An existence theorem for the speed trajectory which corresponds to the absolute minimum is provided. The results are valid for arbitrary Reynolds numbers.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 121 , Issue 1-2 , 1992 , pp. 5 - 32
Copyright
Copyright © Royal Society of Edinburgh 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Krasnosel'skii, M. A. et al. Approximate solutions of operator equations (Moskow: 1969).Google Scholar
2Fattorini, H. and Sritharan, S. S.. Optimal control theory of viscous flow problems (to appear).Google Scholar
3Fleming, W. H.. Future directions in control theory (Philadelphia: SIAM, 1988).Google Scholar
4Hopf, E.. Uber die Aufangswertaufgabe fur die hydrodynamischen Grundgliechungen. Math. Nachr. 4 (1951), 213–231.CrossRefGoogle Scholar
5Ioffe, A. D. and Tihomirov, V. M.. Theory of Extremal problems (Amsterdam: North Holland, 1979).Google Scholar
6Ladyzhenskaya, O. A.. The mathematical theory of viscous incompressible flow, 2nd edn (New York: Gordon and Breach, 1969, English translation).Google Scholar
7Ladyzhenskaya, O. A. and Solonnikov, V. A.. Some problems in vector analysis and generalized formulations of boundary value problems for the Navier-Stokes equations. J. of Soviet Math. 10 (1978), 257–286.CrossRefGoogle Scholar
8Leray, J.. Etude de diverses équations intégrates nonlinéaires et de quelques problémes que pose l'hydrodynamique. J. Math. Pures Appl. 12 (1933), 1–82.Google Scholar
9Lions, J. L.. Optimal control of systems governed by partial differential equations (New York: Springer, 1971).CrossRefGoogle Scholar
10Lions, J. L.. Some Aspects of the optimal control of distributed parameter systems (Philadelphia: SIAM, 1972).CrossRefGoogle Scholar
11Lions, J. L.. Some methods in the mathematical analysis of systems and their control (New York: Gordon and Breach, 1981).Google Scholar
12Lions, J. L. and Magenes, E.. Nonhomogeneous boundary value problems and applications (Berlin: Springer, 1972).Google Scholar
13Sritharan, S. S.. Dynamic programming for the Navier-Stokes equations. In Estimation and Control of Distributed Parameter Systems, ed. Kunish, K., Birkhauser, ISNM 100; 1991.Google Scholar
14Sritharan, S. S.. Pontryagin maximum principle for exterior hydrodynamics. In Optimization and Nonlinear Analysis, ed. Ioffe, A., (Harlow: Longman Publishers, 1991).Google Scholar
15Tanabe, H.. Equations of evolution (London: Pitman, 1979).Google Scholar
16Valent, T.. Boundary Value Problems of Finite Elasticity (New York: Springer, 1988).CrossRefGoogle Scholar