Synchronization and identification of nonlinear systems by using a novel self-evolving interval type-2 fuzzy LSTM-neural network

Abstract

Nonlinear systems widely exist in the real world. Researches on the synchronization and identification of nonlinear systems have both theoretical and practical interests. However, since the pseudo-random and parameter sensitivity, some nonlinear dynamics, such as chaotic systems, are difficult to achieve the required regression approximation. By means of the fuzzy-neural structure and long short-term memory (LSTM) mechanism, this paper proposes a novel inference structure of the self-evolving interval type-2 fuzzy LSTM-neural network (eIT2FNN-LSTM) for the synchronization and identification of nonlinear dynamics. In order to tackle with the time-dependency data generated by nonlinear systems, recurrent neural fuzzy systems with LSTM structure is introduced into type-2 fuzzy neural networks, where, by means of gate mechanism, a recurrent structure in the time dimension by feeding the rule firing strength of each rule back to itself is implemented. Besides, an online rule generation algorithm based on dynamic density clustering is utilized to achieve structural updates, which can meet the need of high frequency data process in reality. By incorporating direct adaptive interval type-2 LSTM fuzzy control scheme and sliding mode approach, two chaotic systems with external disturbance noise or/and random-varying parameters can be synchronized based on Lyapunov stability criterion, where two methods, i.e., the gradient training and particle swarm optimization (PSO) algorithm are used. In order to further verify the universality of the proposed scheme, besides nonlinear system, real-life datasets are also utilized to verify the effectiveness of the proposed fuzzy-neural inference system.