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

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