An Adaptive Multiple Shooting Strategy for Optimal Control

ABSTRACT The use of multiple shooting has become the standard for the numerical solution of optimal control problems. We investigate how multiple shooting affects the convergence properties of Newton‐type methods. For the first time, we conduct a systematic comparison of several multiple shooting strategies on a set of 40 optimal control problems. In addition, we consider differences between interior‐point and sequential quadratic programming methods, accounting for both Quasi‐Newton approximations and exact Hessians. Based on these observations, we propose an adaptive multiple shooting algorithm that reduces the number of iterations by about 27% on average across all problems and by more than 50% for selected problems compared with naïve multiple shooting approaches.