A New Computational Approach for Solving Optimal Control of Linear PDEs Problem

作者：Mahmoudi M^*; Kamyad A V; Effati S

来源：Acta Mathematicae Applicatae Sinica-English Series, 2014, 30(3): 735-748.

DOI：10.1007/s10255-014-0415-7

• optimal control
• parabolic partial differential equation
• semigroups theory
• nonlinear programming
• Toeplitz matrix

In this paper, we present a new computational approach for solving an internal optimal control problem, which is governed by a linear parabolic partial differential equation. Our approach is to approximate the PDE problem by a nonhomogeneous ordinary differential equation system in higher dimension. Then, the homogeneous part of ODES is solved using semigroup theory. In the next step, the convergence of this approach is verified by means of Toeplitz matrix In the rest of the paper, the optimal control problem is solved by utilizing the solution of homogeneous part. Finally, a numerical example is given.

• 出版日期2014