Displaying similar documents to “On the Sensivity and Relaxability of Optimal Control Problems Governed by Nonlinear Evolution Equations with State Constraints.”

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.

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. ...

A nonmonotone line search for the LBFGS method in parabolic optimal control problems

Omid Solaymani Fard, Farhad Sarani, Akbar Hashemi Borzabadi, Hadi Nosratipour (2019)

Kybernetika

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In this paper a nonmonotone limited memory BFGS (NLBFGS) method is applied for approximately solving optimal control problems (OCPs) governed by one-dimensional parabolic partial differential equations. A discretized optimal control problem is obtained by using piecewise linear finite element and well-known backward Euler methods. Afterwards, regarding the implicit function theorem, the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP)....

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...

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 gradient projection method for solving an optimal control problem

M. Farag (1997)

Applicationes Mathematicae

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A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.

Inverse optimal control for linearizable nonlinear systems with input delays

Xiushan Cai, Jie Wu, Xisheng Zhan, Xianhe Zhang (2019)

Kybernetika

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We consider inverse optimal control for linearizable nonlinear systems with input delays based on predictor control. Under a continuously reversible change of variable, a nonlinear system is transferred to a linear system. A predictor control law is designed such that the closed-loop system is asymptotically stable. We show that the basic predictor control is inverse optimal with respect to a differential game. A mechanical system is provided to illustrate the effectiveness of the proposed...

On an optimal control problem for a quasilinear parabolic equation

S. Farag, M. Farag (2000)

Applicationes Mathematicae

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An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.