ABSTRACT
In this paper, we consider the bilinear pseudo-spectral method for solving convection-diffusion optimal control problems (OCPs). First, we convert the optimal control problem to a partial differential equation (PDE) system including the state equation of the original problem and the adjoint equation which must be solved. Next, we approximate the coupled system by a bilinear pseudo-spectral method based on Chebyshev polynomials and obtain a coupled Sylvester system and then use some iterative and direct methods to solve it. We used bilinear pseudo-spectral method to have simplicity in implementation and Chebyshev polynomials to have accuracy and stability. Robustness and accuracy of the method are verified by solving some numerical experiments.
Disclosure statement
No potential conflict of interest was reported by the author(s).