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


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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ISRP Style

Ali Zakeri, Mohammad Masjed-jamei, Amir Hossein Salehi Shayegan, A Numerical Method for Optimal Control-state Problem with Bivariate B-spline Basis, Journal of Mathematics and Computer Science, 8 (2014), no. 4, 335 - 342

AMA Style

Zakeri Ali, Masjed-jamei Mohammad, Shayegan Amir Hossein Salehi, A Numerical Method for Optimal Control-state Problem with Bivariate B-spline Basis. J Math Comput SCI-JM. (2014); 8(4):335 - 342

Chicago/Turabian Style

Zakeri, Ali, Masjed-jamei, Mohammad, Shayegan, Amir Hossein Salehi. "A Numerical Method for Optimal Control-state Problem with Bivariate B-spline Basis." Journal of Mathematics and Computer Science, 8, no. 4 (2014): 335 - 342


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