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Measure solutions for semilinear evolution equations with polynomial growth and their optimal control

N.U. Ahmed (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.

Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control

N.U. Ahmed (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.

Minimax control of nonlinear evolution equations

Nikolaos S. Papageorgiou (1995)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.

On some general almost periodic optimal control problems : links with periodic problems and necessary conditions

Denis Pennequin (2008)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed or variable...

On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions

Denis Pennequin (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed or variable...

On the existence of optimal controls for nonlinear infinite dimensional systems

Antonella Fiacca, Nikolaos S. Papageorgiou, Francesca Papalini (1998)

Czechoslovak Mathematical Journal

We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.

Currently displaying 61 – 80 of 149