发表机构
Santa Clara University（圣克拉拉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于模型的Galerkin提升框架，通过精确LTI分解和残差界，实现非线性系统仅用测量误差的$\mathcal{H}_\infty$输出反馈控制，保证闭环稳定并优于反步法。
AI 中文摘要
本文提出了一种基于模型的Galerkin框架，用于具有已知动力学的非线性系统的输出反馈控制。通过适当的执行器增广，有限维实现保留了执行器动力学和常数输入矩阵。我们将有限阶非闭合性保留为显式加性残差。LTI部分和该残差精确描述了提升后的非线性动力学。该分解不需要可观测量不变子空间，也适用于非控制仿射系统。我们在标准$\mathcal{H}_\infty$设计中使用了闭合残差、执行器实现缺陷和输出重构误差的区域界。所提出的控制器是一个仅由测量跟踪误差驱动的线性动态系统，不需要在线提升。保留状态坐标可给出原始状态的直接界。我们利用这些界推导出先验包含条件。在该条件下，非线性闭环是前向完备的，状态和跟踪误差满足显式瞬态界，并且是一致最终有界的。小车-摆锤示例说明了非线性闭环保证，并将控制器与全状态反步法进行了比较。尽管输出反馈控制器仅使用测量跟踪误差，但其名义跟踪RMSE几乎与反步法相同，且峰值跟踪误差更低。
英文摘要
In this paper, we present a model-based Galerkin framework for output-feedback control of nonlinear systems with known dynamics. With a suitable actuator augmentation, the finite-dimensional realization preserves the actuator dynamics and the constant input matrix. We retain finite-order nonclosure as an explicit additive residual. The LTI part and this residual describe the lifted nonlinear dynamics exactly. The decomposition does not require an invariant subspace of observables and also applies to non-control-affine systems. We use regional bounds on the closure residual, actuator-realization defect, and output-reconstruction error in the standard $\mathcal{H}_\infty$ design. The proposed controller is a linear dynamic system driven only by the measured tracking error and requires no online lifting. Retaining the state coordinates gives direct bounds on the original state. We use these bounds to derive an a priori containment condition. Under this condition, the nonlinear closed loop is forward complete, and the state and tracking error satisfy explicit transient bounds and are uniformly ultimately bounded. The cart-pendulum example illustrates the nonlinear closed-loop guarantees and compares the controller with full-state backstepping. Although the output-feedback controller uses only the measured tracking error, it achieves almost the same nominal tracking RMSE as backstepping, with a lower peak tracking error.
Comments15 pages, 5 figures
