标题： 用于Frenet坐标系中实时车辆控制的深度双线性Koopman模型 显示英文标题

标题： Deep Bilinear Koopman Model for Real-Time Vehicle Control in Frenet Frame

摘要： 由于车辆动力学的非线性和耦合特性，自动驾驶车辆的精确建模和控制仍然是一个基本挑战。 虽然Koopman算子理论提供了一个部署强大线性控制技术的框架，但学习高保真建模的有限维不变子空间仍然是一个开放问题。 本文提出了一种深度Koopman方法，在曲线Frenet坐标系中对车辆动力学进行建模和控制。 所提出的框架使用深度神经网络架构，从数据中同时学习Koopman算子及其相关的不变子空间。 该算法捕获了输入-状态双线性相互作用，同时保持凸性，这使其适用于实时模型预测控制（MPC）应用。 在训练过程中使用多步预测损失以确保长时域预测能力。 为了进一步提高实时轨迹跟踪性能，该模型与累积误差调节器（CER）模块集成，通过减轻累积预测误差来补偿模型不匹配。 通过硬件在环（HIL）实验评估闭环性能，使用CarSim RT模型作为目标被控对象，并在dSPACE SCALEXIO系统上进行实时验证。 所提出的控制器相对于基准控制器显著降低了跟踪误差，证实了其在嵌入式自动驾驶车辆系统中的实时实现适用性。 显示英文摘要

摘要： Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control techniques, learning a finite-dimensional invariant subspace for high-fidelity modeling continues to be an open problem. This paper presents a deep Koopman approach for modeling and control of vehicle dynamics within the curvilinear Frenet frame. The proposed framework uses a deep neural network architecture to simultaneously learn the Koopman operator and its associated invariant subspace from the data. Input-state bilinear interactions are captured by the algorithm while preserving convexity, which makes it suitable for real-time model predictive control (MPC) application. A multi-step prediction loss is utilized during training to ensure long-horizon prediction capability. To further enhance real-time trajectory tracking performance, the model is integrated with a cumulative error regulator (CER) module, which compensates for model mismatch by mitigating accumulated prediction errors. Closed-loop performance is evaluated through hardware-in-the-loop (HIL) experiments using a CarSim RT model as the target plant, with real-time validation conducted on a dSPACE SCALEXIO system. The proposed controller achieved significant reductions in tracking error relative to baseline controllers, confirming its suitability for real-time implementation in embedded autonomous vehicle systems.