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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.

在本研究项目中，将研究用于识别面向控制的非线性经验动态模型的局部仿射多模型类型的鲁棒测试信号设计方法。2014年三个研究小组发表的一篇文章指出，虽然线性模型的实验设计已经得到了深入的研究，但对描述非线性动力系统的模型结构进行实验设计仍然是一个开放的、具有挑战性的研究课题。这是设计问题的主要简化，即，取决于局部模型类型，简化为参数的线性。分区是模型非线性的唯一来源，分区的选择非常重要。在设计过程开始时，分区数量未知，因此无法指定Fisher信息矩阵。对于给定数量的分区，偏导数是复杂的非线性函数，其取决于待识别的参数的值。因此，设计仅针对所选参数值。一个最佳的和强大的实验设计的动态TS模型的分区和局部模型参数的识别是一个困难和有趣的科学问题，以及一个问题的实际relevance.In这个项目的方法，为上述模型类的测试信号设计的发展和检查。这些方法也应该适用于有关目标系统的先验知识很少的情况。它们应该允许识别分区和局部模型参数，并且对于给定的特定识别任务是最佳的（具有很小不确定性的精确模型），并且需要较短的实验持续时间（出于成本原因）。设计问题是棘手的，这样的关键目标是开发方法，以系统地简化问题，这样的最优性是很少妥协，也可以解决大的和病态的问题。一种方法是将联合收割机空间填充与基于模型的设计方法相结合，以便在获得目标系统的更多信息时调整设计。该模型的具体结构用于分解设计问题。这些方法将在模拟研究和试验台上进行测试和演示。实验设计和系统识别领域的共同考虑将提供新的见解和原创性研究成果。