Mittag‐Leffler state estimator design and synchronization analysis for fractional‐order BAM neural networks with time delays

Abstract

Item Type Article Authors Pratap, A.; Dianavinnarasi, J.; Raja, R.; Rajchakit, G.; Cao, J.; Bagdasar, Ovidiu Citation Rajchakit, G., et al (2019) 'Mittag-Leffler state estimator design and synchronization analysis for fractional order BAM neural networks with time delays'. AbstractThis paper deals with the extended design of Mittag-Leffler state estimator and adaptive synchronization for fractional order BAM neural networks (FBNNs) with time delays. By the aid of Lyapunov direct approach and Razumikhin-type method a suitable fractional order Lyapunov functional is constructed and a new set of novel sufficient condition are derived to estimate the neuron states via available output measurements such that the ensuring estimator error system is globally Mittag-Leffler stable. Then, the adaptive feedback control rule is designed, under which the considered FBNNs can achieve Mittag-Leffler adaptive synchronization by means of some fractional order inequality techniques. Moreover, the adaptive feedback control may be utilized even when there is no ideal information from the system parameters. Finally, two numerical simulations are given to reveal the effectiveness of the theoretical consequences.

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

“…8 show the state trajectories of considered systems (38) and (39) respectively. Figures 9-10 present the evaluations of synchronization errors between FCDNNs (38) and isolated networks (39) under the controller (40). Figure 11-12 demonstrate the adaptive feedback control gains (40), which shows that the adaptive control gains may go to some positive constants.…”

“…As a consequence of these benefits, some researchers have shown their keen interest to integrate the FOC into NNs to make fractional-order neural networks (FONNs) models. Among others, the dynamical behaviors of FONNs have already become a hot research topic, and lots of scientific results have been well published in the literature (see [39][40][41][42][43]).…”

“…directed graph G consisting of 4 identical nodes The state trajectories of q 1 (t) vs. p k1 (t) for k = 1, 2, 3, 4 with control(40) …”

“…D h ξ k (t) = 0.95|α k (t)|σ sgn(ξ k (t) -1.004)(40) The state trajectories of q 2 (t) vs. p k2 (t) for k = 1, 2, 3, 4 with control (40) The change processes of synchronization errors with control(40) for k = 1, 2, 3, 4. According to Theorem 3.3, it is simple to check2.5 = β > Λ min (U)nb max v max = 2.3, 3 = ζ > b max w max = 2.625, 2 = η > nd max v max + w max = 1.48,and all the conditions of Theorem 3.3 are satisfied.…”

“…According to Theorem 3.3, it is simple to check2.5 = β > Λ min (U)nb max v max = 2.3, 3 = ζ > b max w max = 2.625, 2 = η > nd max v max + w max = 1.48,and all the conditions of Theorem 3.3 are satisfied. Therefore, FCDNNs(38) and the isolated networks (39) are finite-time synchronized under the discontinuous adaptive feedback control protocol(40). Next, we take the initial values of the discontinuous adaptive feedback control protocol(40) as follows: β 1 (0) = (0.02, 0.03) T , β 2 (0) = (0.03, 0.01) T , β 3 (0) = (0.02, 0.01) T , β 4 (0) = (0.01, 0.02) T , ξ 1 (0) = (0.05, 0.03) T , ξ 2 (0) = (0.04, 0.03) T , ξ 3 (0) = (0.03, 0.04) T , and ξ 4 (0) = (0.02, 0.01) T .…”