Learning-based Adaptive Control using Contraction Theory
This work addresses adaptive control problems for nonlinear systems with uncertainties, offering a novel framework that improves stability and performance, though it appears incremental as it builds on contraction theory and neural networks.
The paper tackles the stability and performance issues in adaptive control when using learned models by introducing a deep learning-based adaptive control framework called adaptive Neural Contraction Metric (aNCM) for nonlinear systems. It demonstrates that aNCM ensures exponential boundedness of trajectory distances under uncertainties and outperforms existing methods in a cart-pole balancing model.
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.