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

在这个研究项目中，一个鲁棒测试信号设计的方法，用于识别面向控制，非线性经验动力学模型的类型的局部仿射多模型将被检查。三个研究组在2014年的一篇文章中指出，虽然线性模型的实验设计已经得到了深入的研究，但描述非线性动力系统的模型结构的实验设计仍然是一个开放和具有挑战性的研究课题。已发表的动态多模型优化实验设计研究假设了给定的划分。这是设计问题的一个主要简化，即依赖于局部模型类型，在参数中减少为线性。分划是模型非线性的唯一来源，分划的选择非常重要。在设计过程的开始，分区的数量是未知的，因此不能指定费雪信息矩阵。对于给定数量的分区，偏导数是依赖于待识别参数值的复杂非线性函数。因此，对于所选的参数值，设计仅是局部的。动态TS模型分区参数和局部模型参数识别的最优鲁棒实验设计是一个困难而有趣的科学问题，也是一个具有实际意义的问题。在本项目中，将开发和研究上述型号的测试信号设计方法。这些方法也应该适用于对目标系统缺乏先验知识的情况。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（具有小不确定性的精确模型）是最佳的，并且需要较短的实验时间（出于成本原因）。设计问题是棘手的，因此关键目标是开发方法，以便系统地简化问题，使最优性很少受到损害，并且也可以解决大型和病态问题。可以采取的一种方法是将空间填充与基于模型的设计方法结合起来，以便随着在目标系统上获得更多信息而调整设计。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考虑将提供新的见解和原创的研究成果。

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.