Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or soft robots. While neural architectures can learn to approximate complex dynamics, they are either limited to low-dimensional systems or provide only limited formal control guarantees due to a lack of embedded physical structure. This paper introduces a latent control framework based on learned structure-preserving reduced-order dynamics for high-dimensional Lagrangian systems. We derive a reduced tracking law for fully actuated systems and adopt a Riemannian perspective on projection-based model-order reduction to study the resulting latent and projected closed-loop dynamics. By quantifying the sources of modeling error, we derive interpretable conditions for stability and convergence. We extend the proposed controller and analysis to underactuated systems by introducing learned actuation patterns. Experimental results on simulated and real-world systems validate our theoretical investigation and the accuracy of our controllers.

翻译：基于模型的控制器通过依赖物理上精确的动态模型，能够提供关于稳定性和收敛性的强保证。然而，对于高维机械系统（如可变形物体或软体机器人），这类模型通常难以获得。虽然神经架构可以学习逼近复杂动力学，但由于缺乏嵌入的物理结构，它们要么仅限于低维系统，要么只能提供有限的形式化控制保证。本文针对高维拉格朗日系统，提出了一种基于学习的结构保持降阶动力学的隐空间控制框架。我们推导了适用于全驱动系统的降阶跟踪律，并采用基于黎曼几何的投影模型降阶视角，以研究由此产生的隐空间及投影闭环动力学。通过量化建模误差的来源，我们推导出了可解释的稳定性与收敛性条件。通过引入学习的驱动模式，我们将所提出的控制器及分析扩展至欠驱动系统。在仿真和真实系统上的实验结果验证了我们的理论探究以及控制器的准确性。