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

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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.