On affine quasi-LPV System Identification with unknown state-scheduling using (deep) Recurrent Neural Networks*

The main contribution of this paper is a model structure for the identification of affine quasi linear parameter-varying (qLPV) models in state-space (SS) form. The special case where the state is unknown and part of the scheduling vector is considered. In this case the model is always recurrent in the states which demands for an internal dynamics approach, e.g. a Recurrent Neural Network (RNN). The proposed approach is based on a structured RNN developed by Lachhab et al. [1], but extends the original model via so-called gates, neural network structures which are responsible for the recent success of RNNs on various areas of application in Machine Learning, such as the Long short-term memory (LSTM) network and the Gated Recurrent Unit (GRU). The use of gates has multiple advantages: The complexity of the models scheduling map and hence its approximation capabilities are increased, while preserving its affine quasi-LPV structure and the applicability of the results on global asymptotic stability (GAS) by Lachhab et al. [1] at the same time. The performance of the proposed approach is demonstrated by comparison with two other RNN-based approaches on two nonlinear system identification benchmark problems.