Yesim SARAC

On solution of an optimal control problem governed by a linear wave equation

This paper studies the minimization problem governed by a wave equation with homogeneous Neumann boundary condition and where the control function is a initial velocity of the system. We give necessary conditions for the existence and uniqueness of the optimal solution. We get the Frechet derivation of the cost functional via the solution of the corresponding adjoint problem. We construct a minimizing sequence and show that the limit of the minimizing sequence is the solution of the optimal control problem.

Keywords:

Wave equation, adjoint problem optimization,

PDF

___

Vasilyev, F.P., Numerical Methods for Solving Extremal Problems, Nauka, Moskow, 1988.
Kowalewski, A., Optimal Control of Distributed hyeperbolic systems with deviating arguments, In. J. Control, 73(11), 1026-1041, 2000.
Lagnesea, J.E. and Leugeringb, G., Time-domain Decomposition of Optimal Control Problems for the Wave equation, System and Control Letters, 48, 229-242, 2003.
Periago, F., Optimal shape and position of the support for the internal exact control of a string, Systems & Control Letters, 58, 136-140, 2009.
Hasanov, A., Simultaneous Determination of the Source Terms in a Linear Hyperbolic Problem from the Final Overdetermination: Weak Solution Approach, IMA J. Appl. Math., 74, pp. 1-19, 2009.
Serovajsky, S., Optimal control for the Systems Described by Hyperbolic Equation with Strong Nonlinearity, Journal of Applied Analysis and Compuation, 3(2), 183-195, 2013.
Kowalewski, A., Optimal Control via Initial State of an Infinite Order Time Delay Hyperbolic System, Proceedings of the 18 ^th International Conference on Process Control, 14-17 June, Tatranska Lomnica, Slovakia, 2011.
Subaşı, M., and Saraç, Y., A Minimizer for Optimizing the Initial Velocity in a Wave Equation, Optimization, 61(3), 327-333, 2012.
Lions, J. L., Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York, 1971.
Ladyzhenskaya, O. A., Boundary Value Problems in Mathematical Physics, Springer, New York, 1985.
Iskenderov, AD, Tagiyev, RQ, Yagubov, QY, Optimization Methods, Çaşıoğlu, Bakü, 2002.