学习耗散动力学：通过构造耗散性的离散时间神经网络
Learning Dissipative Dynamics with Dissipativity-by-Construction Discrete-Time Neural Networks
浏览论文内容
中文总结 AI 辅助
本文提出一种直接基于离散时间深度多层感知器的增量耗散动力学学习方法，通过约束参数化保证构造性耗散性，兼具预测精度与计算效率。
中文摘要 AI 辅助
耗散性是系统理论中的一个基本性质，与稳定性、无源性和输入-输出稳定性密切相关，在机器人学中尤为重要，因为学习到的动力学模型常被嵌入到反馈控制回路中。然而，现有的大多数学习耗散动力学的方法基于连续时间公式，在训练或推理过程中需要ODE求解器，因此计算成本可能很高。此外，由于实际实现本质上是离散时间的，直接离散化连续时间无源系统并不一定能保持无源性，这促使了对显式离散时间保证的需求。本研究提出了一种方法，使用直接在离散时间中制定的深度多层感知器，从输入-输出时间序列数据中学习增量耗散动力学。通过受约束的参数化和专门的训练过程，所提出的模型通过构造而非正则化来保证增量耗散性。基于Lyapunov的分析建立了相应的耗散性和稳定性保证，而对机器人动力系统的模拟表明，与基线方法相比，该模型在预测精度、计算效率和一致保持增量耗散性方面具有竞争力。
英文摘要
Dissipativity is a fundamental system-theoretic property closely related to stability, passivity, and input--output stability, and is particularly important in robotics, where learned dynamics models are often embedded within feedback control loops. However, most existing approaches for learning dissipative dynamics are based on continuous-time formulations, which require ODE solvers during training or inference and can therefore be computationally expensive. Moreover, because practical implementations are inherently discrete-time, direct discretization of a continuous-time passive system does not necessarily preserve passivity, motivating the need for explicit discrete-time guarantees. This study proposes a method for learning incrementally dissipative dynamics from input--output time-series data using a deep multilayer perceptron formulated directly in discrete time. Through a constrained parameterization and a dedicated training procedure, the proposed model guarantees incremental dissipativity by construction rather than through regularization. Lyapunov-based analysis establishes the corresponding dissipativity and stability guarantees, while simulations on robotic dynamical systems demonstrate competitive prediction accuracy, computational efficiency, and consistent preservation of incremental dissipativity compared with baseline methods.
发表机构
- Sungkyunkwan University（成均馆大学）
机构由 AI 辅助整理，请以论文原文为准。
