面向协同设计的事件触发极值搜索
Towards Co-Designed Event-Triggered Extremum Seeking
AI总结：
本文针对带多面体海森不确定性的非线性映射，提出一种联合综合控制器与触发机制的协同设计事件触发极值搜索方法，通过凸优化问题求解，保证系统指数收敛且无芝诺行为，数值结果显示全控制器增益矩阵性能优于对角增益。
AI中文摘要：
本文研究具有多面体海森不确定性的非线性映射的基于梯度的多变量事件触发极值搜索问题。与现有先固定控制器（通常为对角型）再设计触发机制的事件触发极值搜索方法不同，所提方法通过协同设计框架联合综合控制器与触发机制，该框架可同时支持对角型和全控制器增益矩阵。协同设计问题被表述为带有线性矩阵不等式约束的凸优化问题，其解保证平均闭环系统以指定衰减率指数收敛，同时最大化可容许触发阈值以减少通信。李雅普诺夫分析与平均分析确立了事件触发系统的指数稳定性，且证明了其无芝诺行为以保证可实现性。数值结果表明，对角增益无法达到与全控制器增益矩阵相同的触发阈值和衰减率，凸显了利用海森耦合信息的优势。
英文摘要：
This paper studies event-triggered gradient-based multivariable extremum seeking for nonlinear maps with polytopic Hessian uncertainty. Unlike existing event-triggered extremum-seeking methods, which first fix the controller (typically diagonal) and then design the triggering mechanism, the proposed approach jointly synthesizes the controller and the triggering mechanism through a co-design framework that admits both diagonal and full controller gain matrices. The co-design problem is formulated as a convex optimization problem with linear matrix inequality constraints. Its solution guarantees exponential convergence of the average closed-loop system with a prescribed decay rate while maximizing the admissible triggering threshold to reduce communication. Lyapunov and averaging analyses establish exponential stability of the event-triggered system, and Zeno-freeness is proved to guarantee implementability. Numerical results illustrate that diagonal gains cannot achieve the same triggering thresholds and decay rates as the full controller gain matrices, highlighting the benefits of exploiting Hessian coupling information.
