Chebyshev pseudo-spectral method for optimal control problem of Burgers’ equation

Abstract

In this study, an indirect method is proposed based on the Chebyshev pseudo-spectral method for solving optimal control problems governed by Burgers’ equation. Pseudo-spectral methods are one of the most accurate methods for solving nonlinear continuous-time problems, specially optimal control problems. By using optimality conditions, the original optimal control problem is first reduced to a system of partial differential equations with boundary conditions. Control and state functions are then approximated by interpolating polynomials. The convergence is analyzed, and some numerical examples are solved to show the efficiency and capability of the method.

Keywords

• burgers equation
• optimal control
• chebyshev pseudo-spectral method
• chebyshev-gauss-lobatto nodes