Chebyshev pseudospectral method for optimal control problem of Burgers’ equation

In this study, an indirect method is proposed based on the Chebyshev pseudospectral method for solving optimal control problems governed by Burgers’ equation. Pseudospectral methods are one of the most accurate methods for solving nonlinear continuoustime 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.