Displaying similar documents to “Optimal control of systems determined by strongly nonlinear operator valued measures”

Vector and operator valued measures as controls for infinite dimensional systems: optimal control

N.U. Ahmed (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we consider a general class of systems determined by operator valued measures which are assumed to be countably additive in the strong operator topology. This replaces our previous assumption of countable additivity in the uniform operator topology by the weaker assumption. Under the relaxed assumption plus an additional assumption requiring the existence of a dominating measure, we prove some results on existence of solutions and their regularity properties both for linear...

Optimal control of nonlinear evolution equations

Nikolaos S. Papageorgiou, Nikolaos Yannakakis (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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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...

The global control of nonlinear partial differential equations and variational inequalities.

J. E. Rubio (1992)

Extracta Mathematicae

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We study in this note the control of nonlinear diffusion equation and of parabolic variational inequalities by means of an approach which has been proved useful in the analysis of the control of nonlinear ordinary differential equations ([3]) and linear partial differential equations ([2] and [3]). It is based on an idea of Young [7], consisting in the replacement of classical variational problems by problems in measure spaces; its extension to optimal control problems, and the realization...

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

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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.

Optimal control of nonlinear evolution equations associated with time-dependent subdifferentials and applications

Noriaki Yamazaki (2009)

Banach Center Publications

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In this paper we consider optimal control problems for abstract nonlinear evolution equations associated with time-dependent subdifferentials in a real Hilbert space. We prove the existence of an optimal control that minimizes the nonlinear cost functional. Also, we study approximating control problems of our equations. Then, we show the relationship between the original optimal control problem and the approximating ones. Moreover, we give some applications of our abstract results. ...

Optimal control for 2-D nonlinear control systems

Barbara Bily (2002)

Applicationes Mathematicae

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Necessary conditions for some optimal control problem for a nonlinear 2-D system are considered. These conditions can be obtained in the form of a quasimaximum principle.

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

N.U. Ahmed (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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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.

A nonlinear plate control without linearization

Kenan Yildirim, Ismail Kucuk (2017)

Open Mathematics

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In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index...