AI 中文总结
研究多变量非线性系统实时优化，提出离散时间事件触发极值搜索框架，结合离散时间平均与李雅普诺夫分析，证明系统轨迹收敛及平均动态稳定，减少输入更新次数，数值模拟显示其适用于资源感知控制。
AI 中文摘要
本文介绍了一种用于多变量非线性系统实时优化的离散时间事件触发极值搜索框架。与依赖周期性输入更新的传统离散时间极值搜索实现不同，该方案仅在满足状态相关触发条件时才更新控制动作，实现非周期性执行并大幅减少驱动和通信工作量。闭环架构协调了两种结构不同的范式：极值搜索中梯度恢复所需的周期性激励和事件触发控制的非周期性理念。通过结合离散时间平均论证和基于李雅普诺夫的分析，证明了系统轨迹实际收敛到未知极值的邻域，且相应平均动态具有指数稳定性。结果表明，适当设计的触发规则在大幅减少输入更新次数的同时保留了经典极值搜索的基本优化机制。数值模拟表明，用显著更少的驱动事件可实现相当的优化性能，突出了该方法对资源感知数字和网络控制实现的适用性。
英文摘要
This paper introduces a discrete-time event-triggered extremum seeking framework for real-time optimization of multivariable nonlinear systems. In contrast to conventional discrete-time extremum seeking implementations that rely on periodic input updates, the proposed scheme updates the control action only when a state-dependent triggering condition is met, enabling aperiodic execution and substantial reduction of actuation and communication effort. The resulting closed-loop architecture reconciles two structurally different paradigms: the periodic excitation required for gradient recovery in extremum seeking and the aperiodic philosophy of event-triggered control. By combining discrete-time averaging arguments with Lyapunov-based analysis, we prove practical convergence of the system trajectories to a neighborhood of the unknown extremum and exponential stability of the corresponding average dynamics despite the loss of uniform sampling. The results show that appropriately designed triggering rules preserve the essential optimization mechanisms of classical extremum seeking while drastically reducing the number of input updates. Numerical simulations demonstrate that comparable optimization performance can be achieved with significantly fewer actuation events, highlighting the suitability of the method for resource-aware digital and networked control implementations.
Comments15 pages, 2 figures
