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Extremum Seeking Control for Dynamic Maps: A Lie Bracket Averaging Framework

动态映射的极值寻求控制：李括号平均框架

基本信息

批准号：
272118942
负责人：
Professor Dr.-Ing. Christian Ebenbauer
金额：
--
依托单位：
Lehrstuhl für Intelligente Regelungssysteme
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2015
资助国家：
德国
起止时间：
2014-12-31 至 2021-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/272118942?language=en
关键词：
Extremum Seeking Control Dynamic Maps

项目摘要

Extremum seeking is a control method to steer a dynamical system to an extremum (minimum ormaximum) of a partially or completely unknown input-output map associated to a given dynamicalsystem. It has a long history and has found many applications in control problems such as real-time optimization and optimal setpoint regulation in cars, airplanes or in process control.Stability of extremum seeking schemes is often analyzed with the help of classical averaging and singular perturbation theory. Very often, these methods lead to local stability results and the analysis becomes involved in complex extremum seeking tasks such as problems with constraints or unstable plant dynamics. These limitations are not only a drawback for a general theory but also for extending the scope of extremum seeking control to novel applications.Recently, a very promising alternative approach for analyzing extremum seeking schemes basedon Lie bracket averaging techniques has been established by the group of the applicant and their coworkers. The new approach has several advantages. The approach allows to establish strongstability results for extremum seeking schemes and it can be systematically applied to a wide range of problems including extremum seeking problems with manifold constraints as they appear for example in mechanical systems and in synchronization problems. On the other hand, the current results on Lie bracket averaging are mainly limited to static input-output maps. Thus a key advantage of extremum seeking schemes, namely the analysis of dynamic maps, cannot be addressed so far in the Lie bracket averaging approach. Consequently the potential advantages of the new Lie bracket averaging approach in designing advanced extremum seeking schemes, like schemes which can deal with complex constraints and dynamic models, have not been exploited so far. The motivation of this project is to address the above mentioned shortcomings. The goal is to establish a framework for extremum seeking schemes which is based on Lie bracket averaging techniques and which can deal in various ways with dynamic maps and constraints.

极值搜索是一种将动力系统引导到与给定动态系统相关的部分或完全未知的输入-输出映射的极值(最小值或最大值)的控制方法。极值算法有很长的历史，在汽车、飞机或过程控制中的实时优化和最优设定值调节等控制问题中得到了广泛的应用。极值搜索算法的稳定性常常借助于经典的平均和奇异摄动理论进行分析。通常，这些方法会导致局部稳定的结果，并且分析涉及到复杂的极值搜索任务，例如带约束的问题或不稳定的对象动态。这些限制不仅是一般理论的缺陷，也是将极值控制的范围扩展到新的应用的缺陷。最近，申请者和他们的同事们建立了一种非常有前途的基于李括号平均技术的极值寻求方案的分析方法。这种新方法有几个优点。这种方法可以建立极值搜索方案的强稳定性结果，并且可以系统地应用于各种问题，包括具有多种约束的极值搜索问题，例如在机械系统和同步问题中。另一方面，目前关于李括号平均的结果主要局限于静态投入产出映射。因此，极值搜索方案的一个关键优势，即动态地图分析，到目前为止还不能在李括号平均方法中得到解决。因此，新的李括号平均方法在设计高级极值搜索方案方面的潜在优势，如能够处理复杂约束和动态模型的方案，到目前为止还没有得到开发。该项目的动机是解决上述缺陷。目标是建立一个基于李括号平均技术的极值搜索方案的框架，该框架可以以各种方式处理动态映射和约束。

项目成果

期刊论文数量（7）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Model-based extremum seeking for a class of nonlinear systems

DOI：
10.1109/acc.2015.7171031
发表时间：
2015-07
期刊：
2015 American Control Conference (ACC)
影响因子：
0
作者：
Simon Michalowsky;C. Ebenbauer
通讯作者：
Simon Michalowsky;C. Ebenbauer

Extremum Seeking for Time-Varying Functions using Lie Bracket Approximations

DOI：
10.1016/j.ifacol.2017.08.1093
发表时间：
2017-07
期刊：
IFAC-PapersOnLine
影响因子：
0
作者：
V. Grushkovskaya;V. Grushkovskaya;Hans-Bernd Dürr;C. Ebenbauer;A. Zuyev;A. Zuyev
通讯作者：
V. Grushkovskaya;V. Grushkovskaya;Hans-Bernd Dürr;C. Ebenbauer;A. Zuyev;A. Zuyev

Extremum control of linear systems based on output feedback

基于输出反馈的线性系统极限控制