On optimal test signal design for identifying control-oriented dynamical empirical locally linear-affin multi-models

识别面向控制的动态经验局部线性仿射多模型的最优测试信号设计

基本信息

批准号：
335920452
负责人：
Professor Dr.-Ing. Andreas Kroll
金额：
--
依托单位：
Fachgebiet Mess- und Regelungstechnik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2017
资助国家：
德国
起止时间：
2016-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/335920452?language=en
关键词：
optimal test signal design identifying

项目摘要

In this research project methods for a robust test signal design for the identification of control-oriented, nonlinear empirical dynamical models of the type of locally affine multi-models will be examined. An article of three research groups in 2014 says that while experiment design for linear models was thoroughly researched performing experiment design for model structures describing nonlinear dynamical systems is still an open and challenging research topic.Published research on optimal experiment design for dynamical multi-models assumes the partitioning to be given. This is a major simplification of the design problem that is, dependent on the local model type, reduced to be linear in the parameters. The partitioning is the sole source of nonlinearity of the model and its choice is very important. At the beginning of the design process, the number of partitions is unknown such that the Fisher information matrix cannot be specified. For a given number of partitions, the partial derivatives are complex nonlinear functions that depend on the values of the parameters which are to be identified. Therefore the design is only local for the chosen parameter values. An optimal and robust experiment design for the identification of partitioning and local model parameters of dynamical TS models is a difficult and interesting scientific problem as well as a problem of practical relevance.In this project methods for test signal design for the above mentioned model class are to be developed and examined. The methods should be also applicable in case little a-priori knowledge about the target system is available. They should permit to identify partition and local model parameters, and be optimal for the given specific identification task (accurate models with little uncertainty) and require short experiment duration (for cost reasons). The design problem is intractable, such that the key objective is to develop methods in order to systematically simplify the problem such that optimality is little compromised and that also large and ill conditioned problems can be solved. One approach to take is to combine space filling with model-based design methods to permit adjusting the design as more information is gained on the target system. The specific structure of the model is used to decompose the design problem. The methods will be tested and demonstrated in simulation studies and on test stands. The joint consideration of the areas of experiment design and system identification will provide for new insights and original research results.

在此研究项目中，将检查用于识别面向控制的非线性经验动力学模型的稳健测试信号设计的方法。 2014年，三个研究小组的一篇文章说，虽然对线性模型的实验设计进行了彻底研究，该研究对描述非线性动力学系统的模型结构进行了实验设计，仍然是一个开放且具有挑战性的研究主题。发表了有关动态多模型的最佳实验设计的研究，假设给予分区。这是对设计问题的主要简化，它取决于本地模型类型，在参数中缩小为线性。分区是模型非线性的唯一来源，其选择非常重要。在设计过程的开始时，分区的数量尚不清楚，因此无法指定Fisher Information矩阵。对于给定数量的分区，部分导数是复杂的非线性函数，取决于要识别的参数的值。因此，设计仅是所选参数值的局部性。动态TS模型的分区和局部模型参数的最佳和健壮的实验设计是一个困难而有趣的科学问题，也是一个实际相关性的问题。如果可以使用有关目标系统的几乎没有A-Priori知识，则该方法也应适用。他们应允许识别分区和本地模型参数，并对给定的特定识别任务（不确定性的准确模型）非常最佳，并且需要简短的实验持续时间（出于成本原因）。设计问题是棘手的，因此关键目标是为了系统地简化问题，以使最佳性不受损害，并且可以解决大型且条件不佳的问题。一种方法是将填充空间填充与基于模型的设计方法相结合，以允许在目标系统上获得更多信息时调整设计。该模型的特定结构用于分解设计问题。这些方法将在模拟研究和测试架上进行测试和证明。实验设计和系统识别领域的联合考虑将为新的见解和原始研究结果提供。