Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T07:50:22.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Pontryagin's maximum principle for optimal control of a non-well-posed parabolic differential equation involving a state constraint

Published online by Cambridge University Press:  17 February 2009

Mi Jin Lee  and
Jong Yeoul Park
Mi Jin Lee
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609-735, Korea; e-mail:[email protected] and [email protected].
Jong Yeoul Park
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609-735, Korea; e-mail:[email protected] and [email protected].
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 study Pontryagin's maximum principle for some optimal control problems governed by a non-well-posed parabolic differential equation. A new penalty functional is applied to derive Pontryagin's maximum principle and an application for this system is given.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 2 , October 2004 , pp. 171 - 184
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Barbu, V., Analysis and control of nonlinear infinite dimensional systems (Academic Press, Boston, 1993).Google Scholar
[2]Barbu, V., Optimal control of variational inequalities, Pitman Research Notes in Mathematics 100 (Pitman, London, 1994).Google Scholar
[3]Casas, E., Mateos, M. and Raymond, J. P., “Pontryagin's principle for the control of parabolic equations with gradient state constraints”, Nonlinear Anal. 46 (2001) 933–956.CrossRefGoogle Scholar
[4]Li, X. and Yong, J., Optimal control theory for infinite dimensional systems (Birhauser, Boston, 1995).Google Scholar
[5]Lions, J. L., Optimal control of systems governed by partial differential equations (Springer, Berlin, 1971).CrossRefGoogle Scholar
[6]Lions, J. L., Some methods in mathematical analysis of systems and their control (Science Press, Beijing, China, Gordon and Breach, New York, 1981).Google Scholar
[7]Raymond, J. P. and Zidani, H., “Pontryagin's principle for time-optimal problems”, J. Optim. Theory Appl. 101 (1999) 375–402.CrossRefGoogle Scholar
[8]Wang, G. S., “Optimal control problems governed by non-well-posed semilinear elliptic equation”, Nonlinear Anal. 49 (2002) 315–333.CrossRefGoogle Scholar
[9]Wang, G. S., “Pontryagin's maximum principle of optimal control governed by some non-well-posed semilinear parabolic differential equations”, Nonlinear Anal. 53 (2003) 601–618.CrossRefGoogle Scholar
[10]Wang, G. S. and Wang, L., “Maximum principle for optimal control of non-well-posed elliptic differential equations”, Nonlinear Anal. 52 (2003) 41–67.CrossRefGoogle Scholar