Finite time Synchronization of Inertial Memristive Neural Networks with Time Varying Delay

Finite time synchronization control of inertial memristor-based neural networks with varying delay is considered. In view of drive and response concept, the sufficient conditions to ensure finite time synchronization issue of inertial memristive neural networks is given. Based on Lyapunov finite time asymptotic theory, a kind of feedback controllers is designed for inertial memristorbased neural networks to realize the finite time synchronization. Based on Lyapunov stability theory, close loop error system can be proved finite time and fixed time stable. Finally, illustrative example is given to illustrate the effectiveness of theoretical results

Weighted Sum Synchronization of Memristive Coupled Neural Networks

Funding Information: This work is supported by the National Natural Science Foundation of China (No. 61971185) and the Open Fund Project of Key Laboratory in Hunan Universities (No. 18K010). Publisher Copyright: © 2020 Elsevier B.V.It is well known that weighted sum of node states plays an essential role in function implementation of neural networks. Therefore, this paper proposes a new weighted sum synchronization model for memristive neural networks. Unlike the existing synchronization models of memristive neural networks which control each network node to reach synchronization, the proposed model treats the networks as dynamic entireties by weighted sum of node states and makes the entireties instead of each node reach expected synchronization. In this paper, weighted sum complete synchronization and quasi-synchronization are both investigated by designing feedback controller and aperiodically intermittent controller, respectively. Meanwhile, a flexible control scheme is designed for the proposed model by utilizing some switching parameters and can improve anti-interference ability of control system. By applying Lyapunov method and some differential inequalities, some effective criteria are derived to ensure the synchronizations of memristive neural networks. Moreover, the error level of the quasi-synchronization is given. Finally, numerical simulation examples are used to certify the effectiveness of the derived results.Peer reviewe

On general systems with randomly occurring incomplete information

In the system and control community, the incomplete information is generally regarded as the results of (1) our limited knowledge in modelling real-world systems; and (2) the physical constraints on the devices for collecting, transmitting, storing and processing information. In terms of system modelling, the incomplete information typically includes the parameter uncertainties and norm-bounded non-linearities that occur with certain bounds. As for the physical constraints, two well-known examples are the actuator/sensor saturation caused by the limited power/altitude of the devices as well as the signal quantization caused by limited bandwidth for signal propagation

Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations

© 2020 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/.Due to instability being induced easily by parameter disturbances of network systems, this paper investigates the multistability of memristive Cohen-Grossberg neural networks (MCGNNs) under stochastic parameter perturbations. It is demonstrated that stable equilibrium points of MCGNNs can be flexibly located in the odd-sequence or even-sequence regions. Some sufficient conditions are derived to ensure the exponential multistability of MCGNNs under parameter perturbations. It is found that there exist at least (w+2) l (or (w+1) l) exponentially stable equilibrium points in the odd-sequence (or the even-sequence) regions. In the paper, two numerical examples are given to verify the correctness and effectiveness of the obtained results.Peer reviewe

Synchronization of reaction–diffusion Hopfield neural networks with s-delays through sliding mode control

Synchronization of reaction–diffusion Hopfield neural networks with s-delays via sliding mode control (SMC) is investigated in this paper. To begin with, the system is studied in an abstract Hilbert space C([–r; 0];U) rather than usual Euclid space Rn. Then we prove that the state vector of the drive system synchronizes to that of the response system on the switching surface, which relies on equivalent control. Furthermore, we prove that switching surface is the sliding mode area under SMC. Moreover, SMC controller can also force with any initial state to reach the switching surface within finite time, and the approximating time estimate is given explicitly. These criteria are easy to check and have less restrictions, so they can provide solid theoretical guidance for practical design in the future. Three different novel Lyapunov–Krasovskii functionals are used in corresponding proofs. Meanwhile, some inequalities such as Young inequality, Cauchy inequality, Poincaré inequality, Hanalay inequality are applied in these proofs. Finally, an example is given to illustrate the availability of our theoretical result, and the simulation is also carried out based on Runge–Kutta–Chebyshev method through Matlab

Finite-time anti-synchronization of multi-weighted coupled neural networks with and without coupling delays

The multi-weighted coupled neural networks (MWCNNs) models with and without coupling delays are investigated in this paper. Firstly, the finite-time anti-synchronization of MWCNNs with fixed topology and switching topology is analyzed respectively by utilizing Lyapunov functional approach as well as some inequality techniques, and several anti-synchronization criteria are put forward for the considered networks. Furthermore, when the parameter uncertainties appear in MWCNNs, some conditions for ensuring robust finite-time anti-synchronization are obtained. Similarly, we also consider the finite-time anti-synchronization and robust finite-time anti-synchronization for MWCNNs with coupling delays under fixed and switched topologies respectively. Lastly, two numerical examples with simulations are provided to confirm the effectiveness of these derived results

Finite-time stochastic synchronization of fuzzy bi-directional associative memory neural networks with Markovian switching and mixed time delays via intermittent quantized control

We are concerned in this paper with the finite-time synchronization problem for fuzzy bi-directional associative memory neural networks with Markovian switching, discrete-time delay in leakage terms, continuous-time and infinitely distributed delays in transmission terms. After detailed analysis, we come up with an intermittent quantized control for the concerned bi-directional associative memory neural network. By designing an elaborate Lyapunov-Krasovskii functional, we prove under certain additional conditions that the controlled network is stochastically synchronizable in finite time: The 1st moment of every trajectory of the error network system associated to the concerned controlled network tends to zero as time approaches a finite instant (the settling time) which is given explicitly, and remains to be zero constantly thereupon. In the meantime, we present a numerical example to illustrate that the synchronization control designed in this paper is indeed effective. Since the concerned fuzzy network includes Markovian jumping and several types of delays simultaneously, and it can be synchronized in finite time by our suggested control, as well as the suggested intermittent control is quantized which could reduce significantly the control cost, the theoretical results in this paper are rich in mathematical implication and have wide potential applicability in the real world

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

This 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.N/

On State Estimation for Discrete Time-Delayed Memristive Neural Networks Under the WTOD Protocol: A Resilient Set-Membership Approach

In this article, a resilient set-membership approach is put forward to deal with the state estimation problem for a sort of discrete-time memristive neural networks (DMNNs) with hybrid time delays under the weighted try-once-discard protocol (WTODP). The WTODP is utilized to mitigate unnecessary network congestion occurring in the channel between DMNNs and the state estimator. In order to ensure resilience against possible realization errors, the estimator gain is permitted to undergo some norm-bounded parameter drifts. Our objective is to design a resilient set-membership estimator (RSME) that is capable of resisting gain variations and unknown-but-bounded noises by confining the estimation error to certain ellipsoidal regions. By resorting to the recursive matrix inequality technique, sufficient conditions are acquired for the existence of the expected RSME and, subsequently, an optimization problem is formalized by minimizing the constraint ellipsoid (with respect to the estimation error) under WTODP. Finally, numerical simulation is carried out to validate the usefulness of RSME.10.13039/501100001809-National Natural Science Foundation of China (Grant Number: 61873058, 61873148 and 61933007); AHPU Youth Top-Notch Talent Support Program of China (Grant Number: 2018BJRC009); Natural Science Foundation of Universities in Anhui Province of China (Grant Number: gxyqZD2019053); Heilongjiang Postdoctoral Sustentation Fund of China (Grant Number: LBH-Z19048); Royal Society of the U.K.; Alexander von Humboldt Foundation of Germany