Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T10:37:11.027Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimality conditions for systems with insufficient data

Published online by Cambridge University Press:  17 April 2009

Nikolaos S. Papageorgiou
Nikolaos S. Papageorgiou
Affiliation:
University of California, 1015 Department of Mathematics, Davis, California 95616, United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we use the Dubovitski–Milyutin formalism to establish necessary and sufficient conditions for optimality in a nonlinear, distributed parameter control system, with convex cost criterion and initial condition not given a priori (that is it is not a known function but instead it belongs to a specified set). Our result extends a recent theorem of Lions. Finally a concrete example is worked out in detail.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 1 , February 1990 , pp. 45 - 56
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Barbu, V., Nonlinear Semigroups and Differential Equations in Banach Spaces (Noordhoff International Publishing, Leyden, The Netherlands, 1976).CrossRefGoogle Scholar
[2]Dubovitski, A.J. and Milyutin, A., ‘Extremum problems in the presence of restrictions’, U.S.S.R. Comput. Math. and Math. Physics 5 (1965), 1–80.CrossRefGoogle Scholar
[3]Girsanov, I.V., Lectures on Mathematical Theory of Extremum Problems: Lecture Notes in Econom. and Math. Systems 67 (Springer Verlag, Berlin, Heidelberg, New York, 1972).CrossRefGoogle Scholar
[4]Lions, J.-L, Optimal Control of Systems Governed by Partial Differential Equations: Grundlehren Math. Wiss 170 (Springer Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[5]Lions, J.-L., ‘Optimal control of non well-posed distributed systems’, in Mathematical Control Theory, Banach Center Publications, Vol 14, pp. 299–311 (Polish Scientific Publishers, Warsaw, 1985).Google Scholar
[6]Tanabe, H., Equations of Evolution (Pitman, London, 1979).Google Scholar
[7]Wagner, D., ‘Survey of measurable selection theorem’, SIAM J. Control Optim 15 (1977), 859–903.CrossRefGoogle Scholar