基于牛顿法的多变量极值搜索与有界更新速率

中文摘要 AI 辅助

我们提出了一种多变量基于牛顿法的极值搜索方案，其中纳入了更新速率的已知界限。该设计将最近提出的有界极值搜索方案扩展到基于牛顿法的方法，通过估计并求逆Hessian矩阵，使得收敛速率独立于未知的Hessian。作为基于牛顿法算法的重要组成部分，我们设计了一个适当的解调矩阵，以在平均意义上生成Hessian的估计。利用平均分析，证明了有界极值搜索算法对一般多变量静态映射的局部指数稳定性。与之前的实际稳定性结果相比，该算法保证了以具有指数衰减的精确收敛速率收敛到极值点的邻域。随后，在弱Hessian耦合假设下，建立了基于牛顿法的有界极值搜索方法的主要稳定性结果。仿真结果表明，通过使用牛顿法为所有参数分配相等且期望的收敛速率，所提方法相较于有界极值搜索具有优势。

英文摘要

We propose a multivariable Newton-based extremum seeking scheme, incorporating known bounds on update rates. The design extends the recent bounded extremum seeking scheme to the Newton-based approach, which makes the convergence rate independent of the unknown Hessian by estimating and inverting the Hessian matrix. As a vital part of the Newton-based algorithm, we design an appropriate demodulation matrix to generate an estimate of the Hessian in an average sense. The local exponential stability of the bounded extremum seeking algorithm is proven for general multivariable static maps using averaging analysis. In comparison with previous practical stability results, it guarantees convergence to a neighborhood of the extremum point with an exact convergence rate exhibiting exponential decay. Subsequently, the main stability result is established for the Newton-based bounded extremum seeking approach under a weak Hessian coupling assumption. Simulation results demonstrate the advantage of the proposed approach over bounded extremum seeking by assigning equal, desired convergence rates to all parameters using the Newton approach.

发表机构

• Isfahan University of Technology（伊斯法罕理工大学）
• Arak University of Technology（阿拉克理工大学）
• Shahid Beheshti University（沙希德·贝赫什提大学）

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