Auto-regressive multiple-valued logic neurons with sequential Chua’s oscillator back-propagation learning for online prediction and synchronization of chaotic trajectories

Abstract

Purpose – The purpose of this paper is to examine the structural and computational potentials of a powerful class of neural networks (NNs), called multiple-valued logic neural networks (MVLNN), for predicting the behavior of phenomenological systems with highly nonlinear dynamics. MVLNNs are constructed based on the integration of a number of neurons working based on the principle of multiple-valued logics. MVLNNs possess some particular features, namely complex-valued weights, input, and outputs coded by kth roots of unity, and a continuous activation as a mean for transferring numbers from complex spaces to trigonometric spaces, which distinguish them from most of the existing NNs. Design/methodology/approach – The presented study can be categorized into three sections. At the first part, the authors attempt at providing the mathematical formulations required for the implementation of ARX-based MVLNN (AMVLNN). In this context, it is indicated that how the concept of ARX can be used to revise the structure of MVLNN for online applications. Besides, the stepwise formulation for the simulation of Chua’s oscillatory map and multiple-valued logic-based BP are given. Through an analysis, some interesting characteristics of the Chua’s map, including a number of possible attractors of the state and sequences generated as a function of time, are given. Findings – Based on a throughout simulation as well as a comprehensive numerical comparative study, some important features of AMVLNN are demonstrated. The simulation results indicate that AMVLNN can be employed as a tool for the online identification of highly nonlinear dynamic systems. Furthermore, the results show the compatibility of the Chua’s oscillatory system with BP for an effective tuning of the synaptic weights. The results also unveil the potentials of AMVLNN as a fast, robust, and efficient control-oriented model at the heart of NMPC control schemes. Originality/value – This study presents two innovative propositions. First, the structure of MVLNN is modified based on the concept of ARX system identification programming to suit the base structure for coping with chaotic and highly nonlinear systems. Second, the authors share the findings about the learning characteristics of MVLNNs. Through an exhaustive comparative study and considering different rival methodologies, a novel and efficient double-stage learning strategy is proposed which remarkably improves the performance of MVLNNs. Finally, the authors describe the outline of a novel formulation which prepares the proposed AMVLNN for applications in NMPC controllers for dynamic systems.

Stabilizing periodic orbits of Chua’s system using adaptive fuzzy sliding mode controller

“…Chua’s circuit is one of best known nonlinear dynamical systems used to investigate the dynamic behavior in all possible states: periodic, quasi-periodic and chaotic. Although Chua’s circuit is one of the simplest circuits in the literature, it has various complex chaotic dynamic properties which has made it a topic of profound and extensive studies (Chua, 1992; Mozaffari et al , 2015; Tuo, 2016). In the present paper, the proposed technique does not consider Chua’s system as ordinary nonlinear one since it does not treat the stabilization of the unstable equilibrium points of the chaotic system or the tracking of a desired trajectory.…”

Wastewater treatment control method based on a rule adaptive recurrent fuzzy neural network

“…Recently, because of the universal approximation ability for nonlinear mappings, neural networks (Baruch et al , 2005; Dürrenmatt and Gujer, 2012; Chen et al , 2014; Mozaffari et al , 2015; Qiao et al , 2014; Turker, 2008; Zheng et al , 2016) have become a widely used technology for nonlinear systems. However, the structure of NN is always determined by the trial and error methods or evolutionary algorithms, which need lots of time for structure selection.…”