No CrossRef data available.
Article contents
The maximum principle for a type of hereditary semilinear differential equation
Published online by Cambridge University Press: 17 February 2009
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.
An optimal control problem governed by a class of delay semilinear differential equations is studied. The existence of an optimal control is proven, and the maximum principle and approximating schemes are found. As applications, three examples are discussed.
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1994
References
[1]Banks, H. T. and Jacobs, M. Q., “An approach to optimal control of functional differential equations with function space boundary conditions”, J. Differential Equations 13 (1973).CrossRefGoogle Scholar
[2]Barbu, V., “Nonlinear analysis and nonlinear optimal control problems”, manuscript.Google Scholar
[3]Barbu, V., “Convex control problems for linear differential systems of retarded type”, Ricerche Math. 26 (1977) 3–26.Google Scholar
[4]Barbu, V. and Precupanu, T. H., Convexity and optimization in Banach spaces, Editura Academic (Bucuresti/Sijthoff and Noordoff, Groningen, 1978).Google Scholar
[5]Colonius, F., “Necessary optimality conditions for nonlinear hereditary differential systems with function space end constraints”, in Functional Differential Systems and Retarded Topics (ed. Kisielenicz, M.), (The Higher College of Engineering in Zielona Gora, Zielona Gora, Poland, 1980) 62–71.Google Scholar
[6]Ekeland, I., “Nonconvex minimization problems”, Bull. Amer. Soc. 1 (1979) 443–474.CrossRefGoogle Scholar
[7]Fattorini, H. O., “A unified theory of necessary conditions for nonlinear nonconvex control systems”, Appl. Math. Optim. 15 (1987) 141–185.CrossRefGoogle Scholar
[8]Fattorini, H. O. and Sritharan, S. S., “Necessary and sufficient conditions for optimal controls in viscous flow problems”, PAM Report No: 118, University of Colorado, to appear in Proceedings of the Royal Society of Edinburgh Series A.Google Scholar
[9]Ladyzhenskaya, O. A., The mathematical theory of viscous incompressible flow, 2nd ed., English translation (Gordon and Breach, New York, 1969).Google Scholar
[10]Sritharan, S. S., “Dyanamic programming of the Navier-Stokes equation”, Systems and Control Letters 16 (1991) 299–307, North-Holland.CrossRefGoogle Scholar
[11]Temam, R., Navier-Stokes equations, 3rd ed. (North-Holland Publ. Comp., Amsterdam, 1984).Google Scholar
[12]Tiba, D., “Optimal control of nonsmooth distributed parameter systems”, in Lecture notes in mathematics 1459, (Springer-Verlag, Berlin, New York, c. 1990).Google Scholar
You have
Access