基于高斯过程的拉格朗日系统指数稳定投影控制
Exponentially Stable Projector-based Control of Lagrangian Systems with Gaussian Processes
AI总结：
针对拉格朗日系统的非线性不确定性，本文提出一种基于拉格朗日高斯过程的结构保持投影跟踪控制律，利用矩阵分析和收缩理论推导出指数稳定性的概率保证，并通过机械臂仿真验证了其有效性。
摘要：
由于非线性建模不确定性和保守的稳定性准则，为拉格朗日系统设计准确且鲁棒、并具有严格性能保证的跟踪控制器是一项挑战。本文提出了一种基于结构保持投影的跟踪控制律，用于不确定的 Euler-Lagrange (EL) 系统，该控制律采用物理一致的拉格朗日高斯过程。我们利用 L-GP 的不确定性量化进行自适应前馈-反馈平衡。特别地，通过利用矩阵分析结果和收缩理论，推导出了指数稳定性的精确概率保证，其中所提出控制器的优势在收敛速率和半径的闭式表达式中得到了证明和展示。大量数值模拟不仅基于二连杆和软体机械臂证明了控制器的有效性，而且明确分析并验证了所有理论结果。
英文摘要：
Designing accurate yet robust tracking controllers with tight performance guarantees for Lagrangian systems is challenging due to nonlinear modeling uncertainties and conservative stability criteria. This article proposes a structure-preserving projector-based tracking control law for uncertain Euler-Lagrange (EL) systems using physically consistent Lagrangian-Gaussian Processes (L-GPs). We leverage the uncertainty quantification of the L-GP for adaptive feedforward-feedback balancing. In particular, an accurate probabilistic guarantee for exponential stability is derived by leveraging matrix analysis results and contraction theory, where the benefit of the proposed controller is proven and shown in the closed-form expressions for convergence rate and radius. Extensive numerical simulations not only demonstrate the controller's efficacy based on a two-link and a soft robotic manipulator but also all theoretical results are explicitly analyzed and validated.
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