Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach
This work addresses robust control and estimation for nonlinear systems, which is critical for applications like aerospace and robotics, but it appears incremental as it builds on existing contraction metric theory with a deep learning integration.
The paper tackles robust nonlinear estimation and control by introducing a Neural Contraction Metric (NCM) framework, which uses deep learning to approximate optimal contraction metrics, and demonstrates its effectiveness in state estimation and motion planning problems with bounded disturbances.
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.