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

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.

arXiv commentIEEE Control Systems Letters (L-CSS). Preprint version, accepted June 2020

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• Perspectives on Contractivity in Control, Optimization, and Learning
• Incremental Nonlinear Stability Analysis of Stochastic Systems Perturbed by Lévy Noise
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• Guaranteed Trajectory Tracking under Learned Dynamics with Contraction Metrics and Disturbance Estimation
• Neural Contractive Dynamical Systems
• A Two-Part Controller Synthesis Approach for Nonlinear Stochastic Systems Perturbed by Lévy Noise Using Renewal Theory and HJB-Based Impulse Control