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

在这个研究项目中，将研究用于识别面向控制的、局部仿射多模型类型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称，尽管线性模型的实验设计已经得到了深入的研究，但对描述非线性动态系统的模型结构进行实验设计仍然是一个开放和具有挑战性的研究课题。已发表的关于动态多模型最优实验设计的研究假设了划分是给定的。这是对设计问题的重大简化，即依赖于局部模型类型，简化为参数线性。划分是模型非线性的唯一来源，划分的选择非常重要。在设计过程开始时，分区的数量是未知的，因此不能指定Fisher信息矩阵。对于给定数量的分区，偏导数是依赖于要识别的参数的值的复杂非线性函数。因此，该设计仅适用于所选参数值。动态TS模型分区和局部模型参数识别的最优稳健试验设计是一个既困难又有趣的科学问题，也是一个具有实际意义的问题。本项目旨在开发和研究上述模型类的测试信号设计方法。在有关目标系统的先验知识不多的情况下，这些方法也应适用。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(几乎没有不确定性的准确模型)是最优的，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，因此关键的目标是开发方法，以便系统地简化问题，使最优性几乎不受影响，并且还可以解决大的和病态的问题。一种方法是将空间填充与基于模型的设计方法相结合，以便在获得关于目标系统的更多信息时调整设计。利用模型的具体结构对设计问题进行分解。这些方法将在模拟研究和试验台上进行测试和演示。对实验设计和系统识别领域的联合审议将提供新的见解和原创的研究结果。

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.