Jacobi Spectral Collocation Methods For Fractional Optimal Control Problems And Convergence Analysis

In this paper,we present a Jacobi spectral collocation method for fractional op-timal control problems.Firstly,according to the Hamiltonian quantity,we improve the minimal functional corresponding to the optimal control problem,and obtain the necessary condition of the fractional optimal control problem.Combined with the definition of Caputo and Riemann-Liouville derivatives,the equations equivalent to the original problem are deduced.Then we obtain the solution of the nonlinear system equations by using Jacobi spectral collocation method and analyse the con-vergence of this method.Finally,numerical experiments are provided to verify the correctness of the theory and the effectiveness of the method.