Numerical Optimal Control of The Wave Equation

Iranian Journal of Optimization

مقاله 6، دوره 12، شماره 1، شهریور 2020، صفحه 55-62   

نوع مقاله: Technical Note

نویسندگان

Hassan Zarei^{* 1}؛ Ali Zafari²

¹Department of Mathematics, Payame Noor Universiy, Tehran, Iran

²Department of Mathematics Payame Noor University Tehran, Iran

چکیده

In this paper, we present a spectral method for approximating the boundary optimal control problems of a well-known wave equation by the linear optimal control problems. The method is based upon constructing the Mth degree interpolation polynomials, using Chebyshevs nodes, to approximate the wave equation. Necessary conditions for optimal control functions are obtained by using the Pontryagin's maximum principle. Moreover, the control parameterization enhancing technique (CPET) is used to obtain the piecewise constant sub-optimal control functions. Finally, the efficiency of the proposed method is confirmed by a numerical example.

کلیدواژه‌ها

Chebyshev؛ control parameterization؛ optimal control؛ spectral method؛ wave equation