Abstract:

Due to the large discrete errors and low accuracy of the conventional direct collocation method for solving non-smooth optimal control problems, an adaptive direct collocation method is presented. The optimal control problem is transcribed into a nonlinear programming problem by using local piecewise interpolation polynomials to approximate the optimal solution. The estimation method of discrete errors is also presented, and an adaptive mesh refinement algorithm is used to refine the grid by adding nodes to the segments in which the optimal solution is non-smooth, the algorithm is repeated until a userspecified error tolerance is met. Finally, the simulation results demonstrate the utility and efficiency of the proposed method by comparing it with the conventional direct collocation method and the adaptive pseudospectral algorithm respectively.