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

摘要

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