New results on pseudospectral methods for optimal control

In this note, the equivalence between differential and integral pseudospectral methods is justified from the distinctive perspective of Birkhoff interpolation for collocation at the Jacobi-Gauss and flipped Jacobi-Gauss-Radau points. Furthermore, an exact, efficient, and stable approach is presented for computing the associated pseudospectral differentiation/integration matrices even at millions of points. These new results will contribute to the deeper understanding of pseudospectral methods and their practical applications in optimal control.