Identification of nonlinear dynamical systems by means of complex-valued fuzzy-neural multi-model
M. Maya, Ieroham Solomon Baruch · 2017
In this paper, we propose to use the powerful tool of a Fuzzy-Neural Multi-Model, whose structure consists in a Hierarchical methodology composed by: Fuzzyfier, Fuzzy Rule-Based Inference Takagi-Sugeno rules and Defuzzyfier. It is combined with a Complex-Valued Recurrent Neural Network topology. The topology is trained with two recursive learning algorithms, the Back-Propagation and the Levenberg-Marquardt, both expressed in a complex domain. The main objective of system identification of nonlinear oscillatory plants is to issue states and parameters for control. The system identification used only two membership functions (positive and negative) with a small overlap in the neighborhood of zero. In this case, a sinus and square wave are used as input. The simulation results show the comparison between the output of the oscillatory plant (one degree of freedom flexible-joint robot model) and the output of the system identification algorithm. Moreover, the Levenberg-Marquardt algorithm presents some advantages over the Back-Propagation algorithm for the two input signals. The Levenberg-Marquardt minimized cost function (instantaneous Means Squared Error) it is faster than the Back-Propagation. Finally, the comparative simulation results confirm better quality of the Hierarchical Fuzzy-Neural Multi-Model expressed in a complex domain system identification over the simple system identification composed by only Complex-Valued Recurrent Neural Network.