Robust Tracking Control with Neural Network Dynamic Models under Input Perturbations

Robust control problems have significant practical implications since external disturbances can significantly impact the performance of control methods. Existing robust control methods excel at control-affine systems but fail at neural network dynamic models. Developing robust control methods for such systems remains a complex challenge. In this paper, we focus on robust tracking methods for neural network dynamic models. We first propose a reachability analysis tool designed for this system and then introduce how to reformulate a robust tracking problem with reachable sets. In addition, we prove the existence of a feedback policy that bounds the growth of reachable sets over an infinite horizon. The effectiveness of the proposed approach is validated through numerical simulations of the tracking task, where we compare it with a standard tube MPC method.