Optimal control of nonlinear evolution equations

• Autorzy: Nikolaos S. Papageorgiou , Nikolaos Yannakakis
• Języki publikacji: EN

Abstrakty

EN

In this paper, first we consider parametric control systems driven by nonlinear evolution equations defined on an evolution triple of spaces. The parametres are time-varying probability measures (Young measures) defined on a compact metric space. The appropriate optimization problem is a minimax control problem, in which the system analyst minimizes the maximum cost (risk). Under general hypotheses on the data we establish the existence of optimal controls.
Then we pass to nonparametric systems, which are governed by nonlinear evolution equations with nonmonotone operators. We prove two existence results for such evolution inclusions, which are of independent interest and extend significantly the results existing in the literature. Then we solve time-optimal and Meyer-type optimization problems. In Section 5, we derive necessary conditions for saddle point optimality in the minimax control problem. We conclude the paper with three examples of distributed parameter control systems.

Słowa kluczowe

EN

evolution triple; compact embedding; monotone operator; pseudomonotone operator; L-generalized pseudomonotonicity; integration by parts; evolution inclusion; saddle point; necessary conditions; adjoint equation; distributed parameter systems

Kategorie tematyczne

• 49J35: Minimax problems
• 49J27: Problems in abstract spaces
• 34G20: Nonlinear equations
• 49K27: Problems in abstract spaces

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 5-50

Daty

wydano

2001

otrzymano

2000-02-17

Twórcy

autor

Nikolaos S. Papageorgiou

• National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, Greece

autor

Nikolaos Yannakakis

• National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, Greece

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Identyfikatory

DOI

10.7151/dmgt.1016