Mesh Refinement with Early Termination for Dynamic Feasibility Problems

TL;DR

A novel early-terminating mesh refinement strategy using an integrated residual method to solve dynamic feasibility problems and outperforms a conventional refinement method by up to a factor of three in function evaluations.

Abstract

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.

Figures (2)

• Figure 3: Performance comparison based on $\nabla r$ evaluations
• Figure 4: Convergence of the objective function $f$ for each strategy. Mesh refinements appear as sharp kinks.