A Numerical Method for Optimal Control-state Problem with Bivariate B-spline Basis

Volume 8, Issue 4, pp 335 - 342 http://dx.doi.org/10.22436/jmcs.08.04.02

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Authors

Ali Zakeri - Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran. Mohammad Masjed-jamei - Department of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran. Amir Hossein Salehi Shayegan - Department of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran.

Abstract

We apply the bivariate B-spline basis to find an approximate solution for control-state function in a constrained optimal control problem, whose constraint is an elliptic partial differential equation (PDE) with Dirichlet boundary conditions. In this method, the PDE is first discretized and then by using bivariate B-spline basis, a state function is obtained with respect to some unknown coefficients. By applying generalized Newton method, the optimal value for the control function is also determined. Finally, a numerical example is given and the optimal solution is derived by using the bivariate B-spline basis.

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Keywords

• Bivariate B-spline basis
• Optimal control problem
• Elliptic equation
• WEBspline finite element method.

MSC

•  65D07
•  41A15

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