Extremum Seeking for Static Maps With Delays
Extremum Seeking for Static Maps With Delays
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DOI：
10.1109/tac.2016.2564958
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发表时间：
2017-04
影响因子：
6.8
通讯作者：
T. R. Oliveira;M. Krstić;Daisuke Tsubakino
中科院分区：
文献类型：
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作者：
T. R. Oliveira;M. Krstić;Daisuke Tsubakino
本文研究了具有任意长时滞的静态映射的多变量极值求的设计与分析。同时考虑了梯度法和牛顿法。研究了具有不同输入通道时延和输出时延的多输入系统。抖动信号的相位补偿和包含基于扰动（基于平均）的Hessian估计的预测器反馈允许获得局部指数收敛结果到最优点的小邻域，即使在存在延迟的情况下。利用反演变换和无限维平均法对系统进行稳定性分析，捕捉到系统由于时间延迟而产生的无限维状态。特别地，针对具有多个不同输入延迟的基于梯度的极值搜索方案，引入了一种新的类回溯变换来设计预测器。所提出的基于牛顿的极值搜索方法消除了收敛速率对待优化非线性映射的未知Hessian的依赖，与文献中一样，用户可分配且无延迟。一个源寻优示例说明了所提延迟补偿极值寻优方案的性能。
In this paper, we address the design and analysis of multi-variable extremum seeking for static maps subject to arbitrarily long time delays. Both Gradient and Newton-based methods are considered. Multi-input systems with different time delays in each individual input channel as well as output delays are dealt with. The phase compensation of the dither signals and the inclusion of predictor feedback with a perturbation-based (averaging-based) estimate of the Hessian allow to obtain local exponential convergence results to a small neighborhood of the optimal point, even in the presence of delays. The stability analysis is carried out using backstepping transformation and averaging in infinite dimensions, capturing the infinite-dimensional state due the time delay. In particular, a new backstepping-like transformation is introduced to design the predictor for the Gradient-based extremum seeking scheme with multiple and distinct input delays. The proposed Newton-based extremum seeking approach removes the dependence of the convergence rate on the unknown Hessian of the nonlinear map to be optimized, being user-assignable as in the literature free of delays. A source seeking example illustrates the performance of the proposed delay-compensated extremum seeking schemes.