A Chebyshev pseudospectral method for solving fractional-order optimal control problems

This paper presents a new pseudospectral method for solving optimal control problems with fractional orders including state and control input constraints. The proposed method employs an operational matrix of fractional-order differentiation discretizing the feasible optimal solution of the optimal control problem at Chebyshev-Gauss-Lobatto points. Besides, the Clenshaw-Curtis quadrature formula is used to discretize the performance integral. As a result, the optimization problem associated with fractional-order differential equations transforms into a nonlinear programming problem, which can be solved by means of well-developed techniques. The feasibility and effectiveness of the proposed method are illustrated by comparing it with other methods in a numerical example.