In iterative learning control, the control input needed to make the system produce a desired output is obtained by repeated trials. At one extreme, one seeks learning controllers capable of achieving the objective while trying to assume as little knowledge about the system as possible. At the other extreme, if the system can be known completely by identification, then there is no need for learning control because one can simply invert the identified model to produce the necessary control input. Of course, this approach is not practical; perfect identification is impossible even for the simplest case of a linear time-invariant system, as real data invariably contain noise. Realistically, the best answer can be found in the middle ground so that the benefit of each approach can be fully exploited.; The thrust of this thesis that system identification can be used in a manner that is particularly beneficial for the learning control objective. Specific accomplishments contained within this thesis include many theoretical contributions. These include: Introduction of basis functions as a means to identify and control a system in the repetition domain and the tracking and convergence properties of this new learning controller. I also demonstrate experimental results of the learning controller, performed successfully for the first time on a system with many lightly-damped flexibilities. Contained is the development of a modern control optimization format for a learning controller, with both batch and recursive formulations and experimental validation of these algorithms, and the development of a modern reference adaptive control counterpart for learning control and again experimental validation of the learning theory. Finally, the application of system identification and learning Control applied towards general, non-linear systems. In conclusion, I hope to have shown the validity and usefuleness of incorporating ideas from the fields of learning control and system identification into a hybrid class of learning controllers, to create Iterative Learning Control with Basis Functions.
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