论小扰动下非线性静态映射极值搜索的时延鲁棒性

中文摘要 AI 辅助

极值搜索（ES）是一种实时优化策略，因此ES反馈回路中的传输时延对其稳定性有重大影响。ES控制系统能够承受多大的时延？本文为这一问题提供了潜在答案。我们关注基于梯度的ES，用于非线性静态映射，该映射受已知常数时延加上小的时变时延不确定性影响。我们还考虑测量受到小扰动。与大多数现有文献通过预测器反馈处理二次映射时延不同，本文处理更广泛的非二次映射类别，无需任何预测器或观测器进行时延补偿。调制和解调中的抖动信号被精心设计以处理常数时延和时变时延不确定性。当非线性映射未知时，我们提供了ES收敛性和时延鲁棒性的严格分析框架。当非线性映射的一些先验知识可用时，我们能够提供时延和抖动周期的上界的定量估计，以保持ES系统稳定。合适的ES参数选择保证了对于任何大的已知常数时延的实际稳定性。

英文摘要

Extremum seeking (ES) is a real-time optimization strategy, thus transmission delays in the feedback loop of ES have big impact on its stability. How big delay that ES control systems are able to withstand? This paper provides a potential answer to this problem. We focus on gradient-based ES for nonlinear static maps subject to known constant delays plus a small time-varying delay uncertainty. We also consider the measurement to be subject to a small disturbance. Different from a majority of existing literature addressing quadratic maps with delays by predictor feedback, this paper deals with a wider class of non-quadratic maps without any predictor or observer for delay compensation. Dither signals in modulation and demodulation are carefully designed to handle constant delays and time-varying delay uncertainties. When the nonlinear map is unknown, we offer a rigorously analytical framework of ES convergence and delay-robustness. When some a prior knowledge of nonlinear maps is available, we are able to provide a quantitative estimation on upper bounds of time delay and dither periods to keep ES systems to remain stable. A suitable choice of ES parameters guarantees practical stability for any large known constant delay.

发表机构

• School of Information and Control Engineering, Southwest University of Science and Technology（西南科技大学信息与控制工程学院）
• College of Control Science and Engineering, Zhejiang University（浙江大学控制科学与工程学院）

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