A Novel Linear Recurrent Neural Network for Multivariable System Identification

This paper proposes a novel linear recurrent neural network for multivariable system identification, namely a linerec neural network (LNN). Based on this network, the transfer function matrix model of a multivariable system can be identified directly according to its input and output data. In this way, LNNs differ from existing neural networks. An LNN is constructed based on the identification of prior knowledge in a system, and its weights have definite physical meaning. An LNN is equivalent to a linear equation set, and its training algorithm is based on Widrow-Hoff learning rules. In this paper, the theoretical foundation, structural algorithm and learning rules of LNNs are proposed and studied. To guarantee learning convergence, network training stability is analysed using discrete Lyapunov stability theory. Finally, simulation results show the feasibility of LNNs for multivariable system identification.