发表机构
Australian Centre for Robotics (ACFR); School of Aerospace, Mechanical and Mechatronic Engineering（澳大利亚机器人中心; 航空航天、机械与机电工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文提出非线性动力系统鲁棒可逆性概念，通过静态与动态层组合构建鲁棒可逆递归模型及双利普希茨递归平衡网络，经示例展示其在数据驱动控制、学习及流中的应用，可用于鲁棒控制、轨迹优化与复杂轨迹分布建模。
AI 中文摘要
本文提出了非线性动力系统鲁棒可逆性的新概念，并介绍了通过设计实现鲁棒可逆的递归神经网络的构造参数化。我们将鲁棒可逆性定义为存在因果逆系统，使得正向和逆系统都是收缩的，并且具有有界的增量输入输出增益（系统是双利普希茨的），这意味着正向预测和输入重建对信号扰动和初始状态失配都具有鲁棒性。我们通过静态正交层和满足强输入输出单调性的动态层的串联组合构建鲁棒可逆递归模型，并以双利普希茨递归平衡网络（BiLipREN）的形式提供可微神经网络参数化。此外，与动态正交层的组合产生非线性最小相位/全通（即内-外）分解。我们通过在数据驱动的内模控制、动态替代损失学习和信号空间归一化流中的一系列应用示例说明了该框架的实用性，展示了其在鲁棒控制、轨迹优化和复杂轨迹分布生成建模中的效用。
英文摘要
This paper proposes a new notion of robust invertibility for nonlinear dynamical systems, and introduces constructive parameterizations of recurrent neural network which are robustly invertible by design. We define robust invertibility as the existence of a causal inverse system such that both the forward and inverse systems are contracting and have bounded incremental input-output gains (the system is bi-Lipschitz), implying that both forward prediction and input reconstruction are robust to signal perturbations and initial-state mismatch. We construct robustly invertible recurrent models via series composition of static orthogonal layers and dynamic layers satisfying a strong input-output monotonicity property, and provide a differentiable neural network parameterizations in the form of the bi-Lipschitz recurrent equilibrium network (BiLipREN). Additionally, composition with dynamic orthogonal layers yields a nonlinear minimum-phase/all-pass (a.k.a. inner--outer) factorization. We illustrate the utility of the framework through a series of application examples in data-driven internal model control, dynamic surrogate loss learning, and signal-space normalizing flows, illustrating its utility for robust control, trajectory optimization, and generative modeling of complex trajectory distributions.
