Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach

TL;DR

This paper introduces a deep learning framework using Neural Contraction Metrics for robust nonlinear system estimation and control, leveraging convex optimization for stability guarantees and demonstrated on Lorenz oscillator and spacecraft planning.

Contribution

It proposes a novel neural contraction metric approach with a convex optimization foundation for robust nonlinear estimation and control.

Findings

Successfully applied to Lorenz oscillator state estimation.

Effective in spacecraft optimal motion planning.

Provides stability guarantees via convex optimization.

Abstract

This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global approximation of an optimal contraction metric, the existence of which is a necessary and sufficient condition for exponential stability of nonlinear systems. The optimality stems from the fact that the contraction metrics sampled offline are the solutions of a convex optimization problem to minimize an upper bound of the steady-state Euclidean distance between perturbed and unperturbed system trajectories. We demonstrate how to exploit NCMs to design an online optimal estimator and controller for nonlinear systems with bounded disturbances utilizing their duality. The performance of our framework is illustrated through Lorenz oscillator state estimation and spacecraft optimal motion planning problems.