反馈线性化表示的物理信息学习

中文摘要 AI 辅助

反馈线性化是非线性控制中的强大工具，但寻找线性化坐标变换仍然具有挑战性。反馈线性化变换由成熟的偏微分方程（PDE）控制，其适定性基于李代数弗罗贝尼乌斯定理，但对于大系统维度，求解这些偏微分方程在计算上变得难以处理。为解决这一挑战，我们提出了一种级联物理信息神经网络（PINN）框架来近似求解这些偏微分方程。通过分别参数化不同李导数阶数的项，我们减轻了拟合神经网络高阶李导数时固有的复合误差。此外，我们利用学习到的变换设计了一个跟踪控制器，并建立了其相对于学习到的反馈线性化表示不准确性的误差理论界。我们在广泛的反馈可线性化系统上验证了我们的方法，包括一个多输入多输出平面四旋翼飞行器以及解析方法不切实际的合成示例，并证明我们的方法能够在计算上为控制任务发现非线性系统的有效反馈线性化表示。

英文摘要

Feedback linearization is a powerful tool in nonlinear control, but finding the linearizing coordinate transform remains challenging. Feedback linearizing transforms are governed by well-established partial differential equations (PDEs) whose well-posedness is based on the Lie-algebraic Frobenius theorem, but solving the PDEs becomes computationally intractable for large system dimensions. To address this challenge, we propose a cascaded physics-informed neural network (PINN) framework to approximately solve these PDEs. By separately parameterizing terms of different Lie derivative orders, we mitigate the compounding errors inherent in fitting high-order Lie derivatives of neural networks. Furthermore, we use the learned transform to design a tracking controller and establish theoretical bounds on its error with respect to inaccuracies in the learned feedback-linearizing representation. We validate our method on a broad class of feedback linearizable systems, including a multi-input, multi-output planar quadrotor and synthetic examples for which analytical approaches are impractical, and demonstrate that our approach can computationally discover effective feedback-linearizing representations of nonlinear systems for control tasks.

发表机构

• University of Pennsylvania（宾夕法尼亚大学）
• Reality Defender Inc.（Reality Defender 公司）

机构由 AI 辅助整理，请以论文原文为准。