Learning-based Adaptive Control using Contraction Theory

TL;DR

This paper introduces a deep learning-based adaptive control framework called aNCM that ensures stability and robustness for nonlinear systems with uncertainties by approximating real-time Lyapunov function optimization.

Contribution

It presents a novel neural contraction metric that combines deep learning with contraction theory for real-time adaptive control of nonlinear systems.

Findings

Ensures exponential boundedness of system trajectories despite uncertainties.

Demonstrates superior performance over existing methods on a cart-pole model.

Enables real-time implementation of adaptive control laws using DNNs.

Abstract

Adaptive control is subject to stability and performance issues when a learned model is used to enhance its performance. This paper thus presents a deep learning-based adaptive control framework for nonlinear systems with multiplicatively-separable parametrization, called adaptive Neural Contraction Metric (aNCM). The aNCM approximates real-time optimization for computing a differential Lyapunov function and a corresponding stabilizing adaptive control law by using a Deep Neural Network (DNN). The use of DNNs permits real-time implementation of the control law and broad applicability to a variety of nonlinear systems with parametric and nonparametric uncertainties. We show using contraction theory that the aNCM ensures exponential boundedness of the distance between the target and controlled trajectories in the presence of parametric uncertainties of the model, learning errors caused by aNCM approximation, and external disturbances. Its superiority to the existing robust and adaptive control methods is demonstrated using a cart-pole balancing model.