We propose a novel early-terminating mesh refinement strategy using an integrated residual method to solve dynamic feasibility problems. As a generalization of direct collocation, the integrated residual method is used to approximate an infinite-dimensional problem into a sequence of finite-dimensional optimization subproblems. Each subproblem in the sequence is a finer approximation of the previous. It is shown that these subproblems need not be solved to a high precision; instead, an early termination procedure can determine when mesh refinement should be performed. The new refinement strategy, applied to an inverted pendulum swing-up problem, outperforms a conventional refinement method by up to a factor of three in function evaluations.
@article{arxiv.2403.07811,
title = {Mesh Refinement with Early Termination for Dynamic Feasibility Problems},
author = {Eduardo M. G. Vila and Eric C. Kerrigan and Paul Bruce},
journal= {arXiv preprint arXiv:2403.07811},
year = {2024}
}