论文标题
可靠估计和控制的神经收缩指标：凸优化方法
Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach
论文作者
论文摘要
本文使用神经收缩度量（NCM）的概念提出了一个新的基于深度学习的框架，用于鲁棒的非线性估计和控制。 NCM使用了深长的短期记忆复发性神经网络来实现最佳收缩度量的全局近似，其存在是非线性系统指数稳定性的必要条件。最佳性源于以下事实：离线收缩指标是凸优化问题的解决方案，可以最大程度地减少稳态欧几里得距离的上限，而受扰动和未扰动的系统轨迹之间的距离。我们演示了如何利用NCM来设计在线最佳估计器和使用双重性能的非线性系统的最佳估计器和控制器。通过洛伦兹振荡器状态估计和航天器最佳运动计划问题来说明我们的框架的性能。
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.
