Research on efficient and accurate computing strategies for complex optimal control problems

Abstract

In this study, grid refinement strategies are studied to improve computing accuracy and efficiency of the complex optimal control problems. Firstly, a solution method based on multiple variable time nodes was proposed for the optimal control problem with Bang-Bang characteristics. The problem was transformed into the Mayer formula by adding relaxed variables to eliminate integral terms. And the implementation procedure for the algorithm was also defined. Then, for optimal control problems with continuous slope changes and key switching points, a slope-based adaptive grid refinement strategy was also proposed. The time grids were able to automatically increase or decrease based on the slope information, and a new technique was used to judge the switching points and refine the corresponding time grids. Finally, the performances of the proposed methods were verified with six classical examples. The results demonstrate that they comprehensively surpass traditional methods in computing accuracy and efficiency.