虚拟控制收缩度量：通过行为嵌入的凸非线性反馈设计
Virtual Control Contraction Metrics: Convex Nonlinear Feedback Design via Behavioral Embedding
AI总结：
本文提出虚拟控制收缩度量方法，通过行为嵌入和凸优化实现非线性状态反馈控制，统一了全局与局部LPV方法，并为非线性跟踪控制提供严格的指数稳定性和L2增益性能保证。
摘要：
本文提出了一种系统性的非线性状态反馈控制设计方法，具有三个主要优点：（i）它确保相对于用户定义的一组参考轨迹的指数稳定性和 $ \mathcal{L}_2 $-增益性能，（ii）它提供了基于凸优化和基于路径积分的控制实现的构造性条件，（iii）它比以往类似方法限制更少。在所提出的方法中，首先构造非线性动力学的虚拟表示，并为其生成行为（参数变化）嵌入。然后，通过引入虚拟控制收缩度量，推导出凸控制综合公式。最后，计算带有虚拟参考生成器的控制实现，该实现被保证能够针对目标参考行为的所有轨迹实现指数稳定性和 $ \mathcal{L}_2 $-增益性能。我们表明，所提出的方法是线性参数变化（LPV）状态反馈控制方法两个不同类别（全局方法和局部方法）的统一推广。此外，作为非线性跟踪控制的方法，它提供了严格的稳定性和性能保证，而使用标准 LPV 方法的跟踪控制则无法保证这些性质。
英文摘要：
This paper presents a systematic approach to nonlinear state-feedback control design that has three main advantages: (i) it ensures exponential stability and $ \mathcal{L}_2 $-gain performance with respect to a user-defined set of reference trajectories, and (ii) it provides constructive conditions based on convex optimization and a path-integral-based control realization, and (iii) it is less restrictive than previous similar approaches. In the proposed approach, first a virtual representation of the nonlinear dynamics is constructed for which a behavioral (parameter-varying) embedding is generated. Then, by introducing a virtual control contraction metric, a convex control synthesis formulation is derived. Finally, a control realization with a virtual reference generator is computed, which is guaranteed to achieve exponential stability and $ \mathcal{L}_2 $-gain performance for all trajectories of the targeted reference behavior. We show that the proposed methodology is a unified generalization of the two distinct categories of linear-parameter-varying (LPV) state-feedback control approaches: global and local methods. Moreover, it provides rigorous stability and performance guarantees as a method for nonlinear tracking control, while such properties are not guaranteed for tracking control using standard LPV approaches.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
