B‐spline spectral method for constrained fractional optimal control problems

Abstract

In this paper, we present a direct B‐spline spectral collocation method to approximate the solutions of fractional optimal control problems with inequality constraints. We use the location of the maximum of B‐spline functions as collocation points, which leads to sparse and nonsingular matrix B whose entries are the values of B‐spline functions at the collocation points. In this method, both the control and Caputo fractional derivative of the state are approximated by B‐spline functions. The fractional integral of these functions is computed by the Cox‐de Boor recursion formula. The convergence of the method is investigated. Several numerical examples are considered to indicate the efficiency of the method.

Solution of a specific class of nonlinear fractional optimal control problems including multiple delays

“…Some efficient numerical methods for solving fractional differential equations involving delay have been developed in References 10‐17. Several numerical techniques regarding fractional optimal control problems without delay can be found in References 18‐28. Also, some direct methods for solving linear fractional optimal control problems including delay were given in References 29‐33.…”