Continuous-time Dynamic Realization for Nonlinear Stabilization via Control Contraction Metrics

TL;DR

This paper proposes a continuous-time dynamic realization for nonlinear stabilization using control contraction metrics, distributing the computational load over time and enabling real-time application.

Contribution

It introduces a novel dynamic controller that converges to geodesics using covariant derivatives, reducing online optimization complexity.

Findings

The approach effectively computes geodesics in real-time.

Numerical example demonstrates improved computational efficiency.

Method maintains stability while reducing real-time computational burden.

Abstract

Nonlinear stabilization using control contraction metric (CCM) method usually involves an online optimization problem to compute a minimal geodesic (a shortest path) between pair of states, which is not desirable for real-time applications. This paper introduces a continuous-time dynamic realization which distributes the computational cost of the optimization problem over the time domain. The basic idea is to force the internal state of the dynamic controller to converge to a geodesic using covariant derivative information. A numerical example illustrates the proposed approach.