Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems

Abubakar Bello Salati, Mostafa Shamsi, Delfim F. M. Torres

Abstract: Highlights•A general class of fractional optimal control problems was considered, which contains the bang-bang, free final time and path constraints problems.•Fractional integration matrices of Grünwald–Letnikov, trapezoidal and Simpson’s formulas are derived.•Using the fractional integration matrix, the fractional optimal control problems are reduced to a finite-dimensional optimization problem.•In order to improve the speed and accuracy, the gradient of objective function and the Jacobian of constraints are supplied to the optimization solver.•Numerical simulations are provided to illustrate the presented method on different types of fractional optimal control problems.