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Existence of mild solutions on infinite intervals to first order initial value problems for a class of differential inclusions in banach spaces

100%
Benchohra M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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1999
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tom 19
|
nr 1-2
111-121
EN
In this paper we investigate the existence of mild solutions on an unbounded real interval to first order initial value problems for a class of differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.
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Optimal control of nonlinear evolution equations

67%
Papageorgiou N., Yannakakis N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2001
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tom 21
|
nr 1
5-50
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.
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