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On an Optimal Control Problem for the Wave Equation in One Space Dimension Controlled by Third Type Boundary Data

  • Alexey NikitinEmail author
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 44)

Abstract

In the present paper we study the boundary control by the third boundary condition on the left end of a string, the right end being fixed. An optimality criterion based on the minimization of an integral of a linear combination of the control itself and its antiderivative raised to an arbitrary power p≥1 is established. A method is developed permitting one to find a control satisfying this optimality criterion and write it out in the explicit form. The optimal control for p>1 is proved. Thereby proposed optimality criterion uniquely determines the optimal solution of boundary control problem under consideration.

Keywords

Partial differential equations Optimization Integral equations 

Mathematics Subject Classification

49K20 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussian Federation

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