Galerkin method for optimal control of second‐order evolution equations |
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Authors: | Anna Dbiska‐Nagrska Andrzej Just Zdzisaw Stempie |
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Institution: | Anna Dȩbińska‐Nagórska,Andrzej Just,Zdzisaw Stempień |
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Abstract: | This paper presents the Galerkin approximation of the optimization problem of a system governed by non‐linear second‐order evolution equation where a non‐linear operator depends on derivative of the state of the system. The control is acting on a non‐linear equation. After giving some results on the existence of optimal control we shall prove the existence of the weak and strong condensation points of a set of solutions of the approximate optimization problems. Each of these points is a solution of the initial optimization problem. Finally we shall give a simple example using the obtained results. Copyright © 2004 John Wiley & Sons, Ltd. |
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