Learning Tube-Certified Control using Robust Contraction Metrics

TL;DR

This paper introduces a method for jointly learning a robust nonlinear controller and a contraction metric for uncertain systems, ensuring stability and safety with certified trajectory tubes using neural networks.

Contribution

It proposes a novel disturbance rejection objective that certifies tube bounds, enabling robust control and certification for nonlinear systems with disturbances.

Findings

Tighter trajectory tubes achieved compared to previous methods.

Controller is computationally efficient for real-time implementation.

Framework effectively handles bounded disturbances in nonlinear systems.

Abstract

Control design for general nonlinear robotic systems with guaranteed stability and/or safety in the presence of model uncertainties is a challenging problem. Recent efforts attempt to learn a controller and a certificate (e.g., a Lyapunov function or a contraction metric) jointly using neural networks (NNs), in which model uncertainties are generally ignored during the learning process. In this paper, for nonlinear systems subject to bounded disturbances, we present a framework for jointly learning a robust nonlinear controller and a contraction metric using a novel disturbance rejection objective that certifies a tube bound using NNs for user-specified variables (e.g. control inputs). The learned controller aims to minimize the effect of disturbances on the actual trajectories of state and/or input variables from their nominal counterparts while providing certificate tubes around nominal trajectories that are guaranteed to contain actual trajectories in the presence of disturbances. Experimental results demonstrate that our framework can generate tighter (smaller) tubes and a controller that is computationally efficient to implement.