Nonlinear Stabilization via Control Contraction Metrics: a Pseudospectral Approach for Computing Geodesics

TL;DR

This paper introduces a pseudospectral method for efficiently computing geodesics in Control Contraction Metrics, enabling real-time nonlinear stabilization with formal global stability guarantees, bridging the gap between simple and complex control methods.

Contribution

It proposes a novel pseudospectral approach for online geodesic computation in CCM, enhancing real-time nonlinear stabilization with formal guarantees.

Findings

CCM provides tractable offline computations with global stability guarantees.

The pseudospectral method enables rapid online geodesic computation.

CCM controllers outperform LQR and are comparable to NMPC in stability and speed.

Abstract

Real-time nonlinear stabilization techniques are often limited by inefficient or intractable online and/or offline computations, or a lack guarantee for global stability. In this paper, we explore the use of Control Contraction Metrics (CCM) for nonlinear stabilization because it offers tractable offline computations that give formal guarantees for global stability. We provide a method to solve the associated online computation for a CCM controller - a pseudospectral method to find a geodesic. Through a case study of a stiff nonlinear system, we highlight two key benefits: (i) using CCM for nonlinear stabilization and (ii) rapid online computations amenable to real-time implementation. We compare the performance of a CCM controller with other popular feedback control techniques, namely the Linear Quadratic Regulator (LQR) and Nonlinear Model Predictive Control (NMPC). We show that a CCM controller using a pseudospectral approach for online computations is a middle ground between the simplicity of LQR and stability guarantees for NMPC.