A new framework for solving fractional optimal control problems using fractional pseudospectral methods

The main purpose of this work is to provide new fractional pseudospectral methods for solving fractional optimal control problems (FOCPs). We develop differential and integral fractional pseudospectral methods and prove the equivalence between them from the distinctive perspective of Caputo fractional Birkhoff interpolation. As a result, the present work establishes a new unified framework for solving fractional optimal control problems using fractional pseudospectral methods, which can be viewed as an extension of existing frameworks. Furthermore, we provide exact, efficient, and stable approaches to compute the associated fractional pseudospectral differentiation/integration matrices even at millions of Jacobi-type points. Numerical results on two benchmark FOCPs including a fractional bang-bang problem demonstrate the performance of the proposed methods.