Design of state estimator for bidirectional associative memory neural networks with leakage delays

Event-triggered impulsive quasi-synchronization for BAM neural networks with reliable redundant channel

This work addresses the quasi-synchronization of delay master-slave BAM neural networks. To improve the utilization of channel bandwidth, a dynamic event-triggered impulsive mechanism is employed, in which data is transmitted only when a preset event-triggered mechanism or a forced impulse interval is satisfied. In addition, to guarantee the reliability of information transmission, a reliable redundant channel for BAM neural networks is adopted, whose transmission scheduling strategy is designed on the basis of the packet dropouts rate of the main communication channels. Further, an algorithm is employed to reduce the quasi-synchronization range of the error systems and the controllers are obtained. At last, a simulation result is shown to illustrate the effectiveness of the presented strategy.

Resilient Asynchronous State Estimation for Markovian Jump Neural Networks Subject to Stochastic Nonlinearities and Sensor Saturations

This article studies the problem of dissipativity-based asynchronous state estimation for a class of discrete-time Markov jump neural networks subject to randomly occurring nonlinearities, sensor saturations, and stochastic parameter uncertainties. First, two stochastic nonlinearities occurring in the system are described by statistical means and obey two Bernoulli processes independently. Then, the hidden Markov model is used to characterize the real communication environment closely between the designed estimator and the system model due to the networked-induced phenomenons that also lead to randomly occurring parametric uncertainties of the estimator considered modeled by two Bernoulli processes. A new criterion is established to guarantee that the resulting error system is stochastically stable with predefined dissipativity performance. Finally, we provide a simulation example to validate the theoretical analysis.

Global Stability of Bidirectional Associative Memory Neural Networks With Multiple Time-Varying Delays

This article investigates the global stability of bidirectional associative memory neural networks with discrete and distributed time-varying delays (DBAMNNs). By employing the comparison strategy and inequality techniques, global asymptotic stability (GAS) and global exponential stability (GES) of the underlying DBAMNNs are of concern in terms of p -norm ( p ≥ 2 ). Meanwhile, GES of the addressed DBAMNNs is also analyzed in terms of 1-norm. When distributed time delay is neglected, the GES of the corresponding bidirectional associative memory neural networks is presented as an M -matrix, which includes certain existing outcomes as special cases. Two examples are finally provided to substantiate the validity of theories.

Design and Analysis of a Novel Integral Recurrent Neural Network for Solving Time-Varying Sylvester Equation

To solve a general time-varying Sylvester equation, a novel integral recurrent neural network (IRNN) is designed and analyzed. This kind of recurrent neural networks is based on an error-integral design equation and does not need training in advance. The IRNN can achieve global convergence performance and strong robustness if odd-monotonically increasing activation functions [i.e., the linear, bipolar-sigmoid, power, or sigmoid-power activation functions (SP-AFs)] are applied. Specifically, if linear or bipolar-sigmoid activation functions are applied, the IRNN possess exponential convergence performance. The IRNN has finite-time convergence property by using power activation function. To obtain faster convergence performance and finite-time convergence property, an SP-AF is designed. Furthermore, by using the discretization method, the discrete IRNN model and its convergence analysis are also presented. Practical application to robot manipulator and computer simulation results with using different activation functions and design parameters have verified the effectiveness, stability, and reliability of the proposed IRNN.

Outlier-Resistant Remote State Estimation for Recurrent Neural Networks With Mixed Time-Delays

In this brief, a new outlier-resistant state estimation (SE) problem is addressed for a class of recurrent neural networks (RNNs) with mixed time-delays. The mixed time delays comprise both discrete and distributed delays that occur frequently in signal transmissions among artificial neurons. Measurement outputs are sometimes subject to abnormal disturbances (resulting probably from sensor aging/outages/faults/failures and unpredictable environmental changes) leading to measurement outliers that would deteriorate the estimation performance if directly taken into the innovation in the estimator design. We propose to use a certain confidence-dependent saturation function to mitigate the side effects from the measurement outliers on the estimation error dynamics (EEDs). Through using a combination of Lyapunov-Krasovskii functional and inequality manipulations, a delay-dependent criterion is established for the existence of the outlier-resistant state estimator ensuring that the corresponding EED achieves the asymptotic stability with a prescribed H_∞ performance index. Then, the explicit characterization of the estimator gain is obtained by solving a convex optimization problem. Finally, numerical simulation is carried out to demonstrate the usefulness of the derived theoretical results.

Improved approach to the problem of the global Mittag-Leffler synchronization for fractional-order multidimension-valued BAM neural networks based on new inequalities

This paper studies the problem of the global Mittag-Leffler synchronization for fractional-order multidimension-valued BAM neural networks (FOMVBAMNNs) with general activation functions (AFs). First, the unified model is established for the researched systems of FOMVBAMNNs which can be turned into the corresponding multidimension-valued systems as long as the state variables, the connection weights and the AFs of the neural networks are valued to be real, complex, or quaternion. Then, without any decomposition, the criteria in unified form are derived by constructing the new Lyapunov-Krasovskii functionals (LKFs) in vector form, combining two new inequalities and considering the easy controllers. It is worth mentioning that the obtained criteria have many advantages in higher flexibility, more diversity, smaller computation, and lower conservatism. Finally, a simulation example is provided to illustrate the availability and improvements of the acquired results.

Stubborn State Estimation for Delayed Neural Networks Using Saturating Output Errors

This paper is concerned with the stubborn state estimation of delayed neural networks that subject to a general class of disturbances in measurements, including outliers and impulsive disturbances as its special cases. This class of disturbances may be unbounded, irregular, and assorted; therefore, they can hardly be suppressed by existing identification-based estimation approaches. In this paper, a stubborn state estimator is constructed by intentionally devising a saturation scheme on the injection of output estimation error. The embedded saturation can effectively resist the influences from these measurement disturbances by saturating them. Moreover, the saturation threshold in the designed scheme is not constant but governed by a dynamic equation with parameters to be designed. Benefiting from this adaptiveness, the estimator obtains more freedom in dealing with various disturbances. By combining a novel Lyapunov functional, the generalized sector condition and two latest integral inequalities, a delay-dependent criterion is derived in a less conservative way to check whether the estimation error system with this dynamic saturation is globally stable. A sufficient condition with two tuning scalars is further provided to codesign the gain of the state estimator and the evolution law of the saturation threshold. Finally, two numerical examples are used to illustrate the stubbornness of this state estimator in the presence of measurement outliers or impulsive disturbances.

An Arcak-type state estimation design for time-delayed static neural networks with leakage term based on unified criteria

The issue of unified dissipativity-based Arcak-type state estimator design for delayed static neural networks (SNNs) with leakage term and noise distraction was considered here. An Arcak-type state observer, which is compact than the usually used Luenberger-type state estimator, is selected to implement the subject of a unified dissipativity performance of SNNs. This paper primarily concentrates on the issue of Arcak-type state estimator of delayed SNNs involving leakage delay. The first attempt is made to tackle the Arcak-type state estimator of SNNs with time delay in leakage term in this paper based on the unified criteria, by constructing a novel Lyapunov functional together with newly improved integral inequalities. As a result, a novel unified state estimation criterion is launched in the form of linear matrix inequalities (LMIs) and put forward to justify the dynamics of error system is extended dissipative with the influence of leakage term and estimator gain matrices K¯₁ and K¯₂. Finally, an interesting simulation study is ultimately explored to show the performance of the established unified dissipativity-based theoretical results, in which, comparison results are also made together with recent works as a special case.

Quantum-Inspired Multidirectional Associative Memory With a Self-Convergent Iterative Learning

Quantum-inspired computing is an emerging research area, which has significantly improved the capabilities of conventional algorithms. In general, quantum-inspired hopfield associative memory (QHAM) has demonstrated quantum information processing in neural structures. This has resulted in an exponential increase in storage capacity while explaining the extensive memory, and it has the potential to illustrate the dynamics of neurons in the human brain when viewed from quantum mechanics perspective although the application of QHAM is limited as an autoassociation. We introduce a quantum-inspired multidirectional associative memory (QMAM) with a one-shot learning model, and QMAM with a self-convergent iterative learning model (IQMAM) based on QHAM in this paper. The self-convergent iterative learning enables the network to progressively develop a resonance state, from inputs to outputs. The simulation experiments demonstrate the advantages of QMAM and IQMAM, especially the stability to recall reliability.

Robust Estimation for Neural Networks With Randomly Occurring Distributed Delays and Markovian Jump Coupling

This paper studies the issue of robust state estimation for coupled neural networks with parameter uncertainty and randomly occurring distributed delays, where the polytopic model is employed to describe the parameter uncertainty. A set of Bernoulli processes with different stochastic properties are introduced to model the randomly occurrences of the distributed delays. Novel state estimators based on the local coupling structure are proposed to make full use of the coupling information. The augmented estimation error system is obtained based on the Kronecker product. A new Lyapunov function, which depends both on the polytopic uncertainty and the coupling information, is introduced to reduce the conservatism. Sufficient conditions, which guarantee the stochastic stability and the performance of the augmented estimation error system, are established. Then, the estimator gains are further obtained on the basis of these conditions. Finally, a numerical example is used to prove the effectiveness of the results.

Finite-Time State Estimation for Recurrent Delayed Neural Networks With Component-Based Event-Triggering Protocol

This paper deals with the event-based finite-time state estimation problem for a class of discrete-time stochastic neural networks with mixed discrete and distributed time delays. In order to mitigate the burden of data communication, a general component-based event-triggered transmission mechanism is proposed to determine whether the measurement output should be released to the estimator at certain time-point according to a specific triggering condition. A new concept of finite-time boundedness in the mean square is put forward to quantify the estimation performance by introducing a settling-like time function. The objective of the addressed problem is to construct an event-based state estimator to estimate the neuron states such that, in the presence of both mixed time delays and external noise disturbances, the dynamics of the estimation error is finite-time bounded in the mean square with a prescribed error upper bound. Sufficient conditions are established, via stochastic analysis techniques, to guarantee the desired estimation performance. By solving an optimization problem with some inequality constraints, the explicit expression of the estimator gain matrix is characterized to minimize the settling-like time. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed estimator design scheme.

Sampled-Data Stabilization for Fuzzy Genetic Regulatory Networks with Leakage Delays

This paper deals with the sampled-data stabilization problem for Takagi-Sugeno (T-S) fuzzy genetic regulatory networks with leakage delays. A novel Lyapunov-Krasovskii functional (LKF) is established by the non-uniform division of the delay intervals with triplex and quadruplex integral terms. Using such LKFs for constant and time-varying delay cases, new stability conditions are obtained in the T-S fuzzy framework. Based on this, a new condition for the sampled-data controller design is proposed using a linear matrix inequality representation. A numerical result is provided to show the effectiveness and potential of the developed design method.

Impact of leakage delay on bifurcation in high-order fractional BAM neural networks

The effects of leakage delay on the dynamics of neural networks with integer-order have lately been received considerable attention. It has been confirmed that fractional neural networks more appropriately uncover the dynamical properties of neural networks, but the results of fractional neural networks with leakage delay are relatively few. This paper primarily concentrates on the issue of bifurcation for high-order fractional bidirectional associative memory(BAM) neural networks involving leakage delay. The first attempt is made to tackle the stability and bifurcation of high-order fractional BAM neural networks with time delay in leakage terms in this paper. The conditions for the appearance of bifurcation for the proposed systems with leakage delay are firstly established by adopting time delay as a bifurcation parameter. Then, the bifurcation criteria of such system without leakage delay are successfully acquired. Comparative analysis wondrously detects that the stability performance of the proposed high-order fractional neural networks is critically weakened by leakage delay, they cannot be overlooked. Numerical examples are ultimately exhibited to attest the efficiency of the theoretical results.

Impulsive Multisynchronization of Coupled Multistable Neural Networks With Time-Varying Delay

This paper studies the synchronization problem of coupled delayed multistable neural networks (NNs) with directed topology. To begin with, several sufficient conditions are developed in terms of algebraic inequalities such that every subnetwork has multiple locally exponentially stable periodic orbits or equilibrium points. Then two new concepts named dynamical multisynchronization (DMS) and static multisynchronization (SMS) are introduced to describe the two novel kinds of synchronization manifolds. Using the impulsive control strategy and the Razumikhin-type technique, some sufficient conditions for both the DMS and the SMS of the controlled coupled delayed multistable NNs with fixed and switching topologies are derived, respectively. Simulation examples are presented to illustrate the effectiveness of the proposed results.

Global asymptotic stability of complex-valued neural networks with additive time-varying delays

In this paper, we extensively study the global asymptotic stability problem of complex-valued neural networks with leakage delay and additive time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and applying newly developed complex valued integral inequalities, sufficient conditions for the global asymptotic stability of proposed neural networks are established in the form of complex-valued linear matrix inequalities. This linear matrix inequalities are efficiently solved by using standard available numerical packages. Finally, three numerical examples are given to demonstrate the effectiveness of the theoretical results.

New delay-interval-dependent stability criteria for switched Hopfield neural networks of neutral type with successive time-varying delay components

This paper deals with the problem of delay-interval-dependent stability criteria for switched Hopfield neural networks of neutral type with successive time-varying delay components. A novel Lyapunov-Krasovskii (L-K) functionals with triple integral terms which involves more information on the state vectors of the neural networks and upper bound of the successive time-varying delays is constructed. By using the famous Jensen's inequality, Wirtinger double integral inequality, introducing of some zero equations and using the reciprocal convex combination technique and Finsler's lemma, a novel delay-interval dependent stability criterion is derived in terms of linear matrix inequalities, which can be efficiently solved via standard numerical software. Moreover, it is also assumed that the lower bound of the successive leakage and discrete time-varying delays is not restricted to be zero. In addition, the obtained condition shows potential advantages over the existing ones since no useful term is ignored throughout the estimate of upper bound of the derivative of L-K functional. Using several examples, it is shown that the proposed stabilization theorem is asymptotically stable. Finally, illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed approach with a four-tank benchmark real-world problem.

Exponential Stability and Stabilization of Delayed Memristive Neural Networks Based on Quadratic Convex Combination Method

This paper is concerned with the exponential stability and stabilization of memristive neural networks (MNNs) with delays. First, we present some generalized double-integral inequalities, which include some existing inequalities as their special cases. Second, combining with quadratic convex combination method, these double-integral inequalities are employed to formulate a delay-dependent stability condition for MNNs with delays. Third, a state-dependent switching control law is obtained for MNNs with delays based on the proposed stability conditions. The desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities. Finally, the feasibility and effectiveness of the proposed results are tested by two numerical examples.

Passivity of memristor-based BAM neural networks with different memductance and uncertain delays

This paper addresses the passivity problem for a class of memristor-based bidirectional associate memory (BAM) neural networks with uncertain time-varying delays. In particular, the proposed memristive BAM neural networks is formulated with two different types of memductance functions. By constructing proper Lyapunov-Krasovskii functional and using differential inclusions theory, a new set of sufficient condition is obtained in terms of linear matrix inequalities which guarantee the passivity criteria for the considered neural networks. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theoretical results.