A Mesh Refinement Algorithm for Solving Optimal Control Problems Using Pseudospectral Methods

A state approximation-mesh refinement algorithm is presented for determining solutions to optimal control problems using pseudospectral methods. In the method presented in this paper the polynomial approximation of the state is used to assess the difference between consecutive selections of the number of segments and the number of collocation point within each segment to determine better combinations of segments and collocation points on the subsequent grid. This process of computing the difference between polynomial approximations is continued until the difference lies below a user-specified threshold. Because the method developed in this paper combines dividing the problem into segments and determining the best number of collocation points within each segment, the approach conceived here is termed a hybrid global/local collocation method. The user-specified parameters of the method are provided and the approach is demonstrated successfully on four optimal control problems of varying complexity. It is found that the hybrid approach developed in this paper leads to a greater accuracy with lower overall computational time as compared to using a purely global approach.