Fractional Pseudospectral Schemes With Applications to Fractional Optimal Control Problems

Abstract

This research endeavors to introduce novel fractional pseudospectral methodologies tailored for addressing fractional optimal control problems encompassing inequality constraints and boundary conditions. Leveraging fractional Lagrange interpolation functions, we formulate differential and integral pseudospectral matrices pivotal in discretizing fractional optimal control problems. The stability of these matrices is ensured through the utilization of Müntz–Legendre polynomials. Discretization of fractional optimal control problems entails employing integral and differential fractional matrices, with collocation strategically positioned at both Gauss and flipped Radau‐type points. Our results demonstrate that the proposed method is well suited for practical problems with larger domains. Furthermore, it proves effective for Bang‐Bang type problems and offers substantial benefits for problems with nonsmooth solutions. Comprehensive numerical evaluations on benchmark fractional optimal control problems substantiate the effectiveness of the devised pseudospectral methodologies, showcasing their commendable performance and potential for practical applications.