Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Multi-periodicity of switched neural networks with time delays and periodic external inputs under stochastic disturbances

This paper presents new theoretical results on the multi-periodicity of recurrent neural networks with time delays evoked by periodic inputs under stochastic disturbances and state-dependent switching. Based on the geometric properties of activation function and switching threshold, the neuronal state space is partitioned into 5ⁿ regions in which 3ⁿ ones are shown to be positively invariant with probability one. Furthermore, by using Itô's formula, Lyapunov functional method, and the contraction mapping theorem, two criteria are proposed to ascertain the existence and mean-square exponential stability of a periodic orbit in every positive invariant set. As a result, the number of mean-square exponentially stable periodic orbits increases to 3ⁿ from 2ⁿ in a neural network without switching. Two illustrative examples are elaborated to substantiate the efficacy and characteristics of the theoretical results.

Multiple and Complete Stability of Recurrent Neural Networks With Sinusoidal Activation Function

This article presents new theoretical results on multistability and complete stability of recurrent neural networks with a sinusoidal activation function. Sufficient criteria are provided for ascertaining the stability of recurrent neural networks with various numbers of equilibria, such as a unique equilibrium, finite, and countably infinite numbers of equilibria. Multiple exponential stability criteria of equilibria are derived, and the attraction basins of equilibria are estimated. Furthermore, criteria for complete stability and instability of equilibria are derived for recurrent neural networks without time delay. In contrast to the existing stability results with a finite number of equilibria, the new criteria, herein, are applicable for both finite and countably infinite numbers of equilibria. Two illustrative examples with finite and countably infinite numbers of equilibria are elaborated to substantiate the results.

On Complete Stability of Recurrent Neural Networks With Time-Varying Delays and General Piecewise Linear Activation Functions

This paper addresses the problem of complete stability of delayed recurrent neural networks with a general class of piecewise linear activation functions. By applying an appropriate partition of the state space and iterating the defined bounding functions, some sufficient conditions are obtained to ensure that an n -neuron neural network is completely stable with exactly ∏_i=1ⁿ(2K_i-1) equilibrium points, among which ∏_i=1ⁿK_i equilibrium points are locally exponentially stable and the others are unstable, where K_i (i=1,…,n) are non-negative integers which depend jointly on activation functions and parameters of neural networks. The results of this paper include the existing works on the stability analysis of recurrent neural networks with piecewise linear functions as special cases and hence can be considered as the improvement and extension of the existing stability results in the literature. A numerical example is provided to illustrate the derived theoretical results.

Resilient fault-tolerant anti-synchronization for stochastic delayed reaction-diffusion neural networks with semi-Markov jump parameters

This paper deals with the anti-synchronization issue for stochastic delayed reaction-diffusion neural networks subject to semi-Markov jump parameters. A resilient fault-tolerant controller is utilized to ensure the anti-synchronization in the presence of actuator failures as well as gain perturbations, simultaneously. Firstly, by means of the Lyapunov functional and stochastic analysis methods, a mean-square exponential stability criterion is derived for the resulting error system. It is shown the obtained criterion improves a previously reported result. Then, based on the present analysis result and using several decoupling techniques, a strategy for designing the desired resilient fault-tolerant controller is proposed. At last, two numerical examples are given to illustrate the superiority of the present stability analysis method and the applicability of the proposed resilient fault-tolerant anti-synchronization control strategy, respectively.

Finite-time and fixed-time anti-synchronization of Markovian neural networks with stochastic disturbances via switching control

This paper proposes a unified theoretical framework to study the problem of finite/fixed-time drive-response anti-synchronization for a class of Markovian stochastic neural networks. State feedback switching controllers without the sign function are designed to achieve the finite/fixed-time anti-synchronization of the addressed systems. Compared with the existing synchronization criteria, our results indicate that the controllers via the switching control without the sign function are given with less conservativeness, and the controllers without any sign function can deal with the chattering problem. By employing Lyapunov functional method and properties of the Weiner process, several finite/fixed-time synchronization criteria are presented and the corresponding settling times are calculated as well. Finally, three numerical examples are provided to illustrate the effectiveness of the theoretical results.

Synchronization of Multiple Reaction-Diffusion Neural Networks With Heterogeneous and Unbounded Time-Varying Delays

The synchronization problem of multiple/coupled reaction-diffusion neural networks with time-varying delays is investigated. Differing from the existing considerations, state delays among distinct neurons and coupling delays among different subnetworks are included in the proposed model, the assumptions posed on the arisen delays are very weak, time-varying, heterogeneous, even unbounded delays are permitted. To overcome the difficulties from this kind of delay as well as diffusion effects, a comparison-based approach is applied to this model and a series of algebraic criteria are successfully obtained to verify the global asymptotical synchronization. By specifying the existing delays, some M -matrix-based criteria are derived to justify the power-rate synchronization and exponential synchronization. In addition, new criterion on synchronization of general connected neural networks without diffusion effects is also given. Finally, two simulation examples are given to verify the effectiveness of the obtained theoretical results and provide a comparison with the existing criterion.

Global Synchronization of Coupled Fractional-Order Recurrent Neural Networks

This paper presents new theoretical results on the global synchronization of coupled fractional-order recurrent neural networks. Under the assumptions that the coupled fractional-order recurrent neural networks are sequentially connected in form of a single spanning tree or multiple spanning trees, two sets of sufficient conditions are derived for ascertaining the global synchronization by using the properties of Mittag-Leffler function and stochastic matrices. Compared with existing works, the results herein are applicable for fractional-order systems, which could be viewed as an extension of integer-order ones. Two numerical examples are presented to illustrate the effectiveness and characteristics of the theoretical results.

Distributed Adaptive Tracking Synchronization for Coupled Reaction-Diffusion Neural Network

This paper considers the tracking synchronization problem for a class of coupled reaction-diffusion neural networks (CRDNNs) with undirected topology. For the case where the tracking trajectory has identical individual dynamic as that of the network nodes, the edge-based and vertex-based adaptive strategies on coupling strengths as well as adaptive controllers, which demand merely the local neighbor information, are proposed to synchronize the CRDNNs to the tracking trajectory. To reduce the control costs, an adaptive pinning control technique is employed. For the case where the tracking trajectory has different individual dynamic from that of the network nodes, the vertex-based adaptive strategy is proposed to drive the synchronization error to a relatively small area, which is adjustable according to the parameters of the adaptive strategy. This kind of adaptive design can enhance the robustness of the network against the external disturbance posed on the tracking trajectory. The obtained theoretical results are verified by two representative examples.

New Stability Criterion for Continuous-Time Takagi-Sugeno Fuzzy Systems With Time-Varying Delay

In this technical paper, a new Lyapunov-Krasovskii functional (LKF) is designed to study the stability of continuous-time Takagi-Sugeno fuzzy systems with time-varying delay. The integrand of the LKF depends on integral variable and time t which can help to reduce the number of linear matrix inequalities (LMIs). Then, a new stability criterion is derived by analyzing the sign of the time derivatives of membership functions. Compared with the existing results, larger delay bounds can be obtained by applying the new criterion. In the end, two examples show the effectiveness of the conclusions.

Exponential Stability Analysis for Delayed Semi-Markovian Recurrent Neural Networks: A Homogeneous Polynomial Approach

This paper investigates the exponential stability analysis issue for a class of delayed recurrent neural networks (RNNs) with semi-Markovian parameters. By constructing a stochastic Lyapunov functional and using some zoom techniques to estimate its weak infinitesimal operator, the exponential mean square stability criteria have been proposed for the Markovian neural networks with certain transition probabilities. We then generalize the homogeneous polynomial approach for the delayed Markovian RNNs with uncertain transition probabilities during the stability analysis. Theoretical results have obtained by introducing an appropriate technique for dealing with a large number of complex homogeneous polynomial matrix inequalities. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed technique.

Adaptive Asymptotic Neural Network Control of Nonlinear Systems With Unknown Actuator Quantization

In this paper, we propose an adaptive neural-network-based asymptotic control algorithm for a class of nonlinear systems subject to unknown actuator quantization. To this end, we exploit the sector property of the quantization nonlinearity and transform actuator quantization control problem into analyzing its upper bounds, which are then handled by a dynamic loop gain function-based approach. In our adaptive control scheme, there is only one parameter required to be estimated online for updating weights of neural networks. Within the framework of Lyapunov theory, it is shown that the proposed algorithm ensures that all the signals in the closed-loop system are ultimately bounded. Moreover, an asymptotic tracking error is obtained by means of introducing Barbalat's lemma to the proposed adaptive law.

th Moment Exponential Input-to-State Stability of Delayed Recurrent Neural Networks With Markovian Switching via Vector Lyapunov Function

In this paper, the th moment input-to-state exponential stability for delayed recurrent neural networks (DRNNs) with Markovian switching is studied. By using stochastic analysis techniques and classical Razumikhin techniques, a generalized vector -operator differential inequality including cross item is obtained. Without additional restrictive conditions on the time-varying delay, the sufficient criteria on the th moment input-to-state exponential stability for DRNNs with Markovian switching are derived by means of the vector -operator differential inequality. When the input is zero, an improved criterion on exponential stability is obtained. Two numerical examples are provided to examine the correctness of the derived results.

Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay

Continuous-time semi-Markovian jump neural networks (semi-MJNNs) are those MJNNs whose transition rates are not constant but depend on the random sojourn time. Addressing stochastic synchronization of semi-MJNNs with time-varying delay, an improved stochastic stability criterion is derived in this paper to guarantee stochastic synchronization of the response systems with the drive systems. This is achieved through constructing a semi-Markovian Lyapunov-Krasovskii functional together as well as making use of a novel integral inequality and the characteristics of cumulative distribution functions. Then, with a linearization procedure, controller synthesis is carried out for stochastic synchronization of the drive-response systems. The desired state-feedback controller gains can be determined by solving a linear matrix inequality-based optimization problem. Simulation studies are carried out to demonstrate the effectiveness and less conservatism of the presented approach.

Global exponential stability of Markovian jumping stochastic impulsive uncertain BAM neural networks with leakage, mixed time delays, and α-inverse Hölder activation functions

This paper concerns the problem of enhanced results on robust finite time passivity for uncertain discrete time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, reciprocally convex combination method, and linear matrix inequality technique, we derive several sufficient conditions for varying the passivity of discrete time BAM neural networks. Further, some sufficient conditions for finite time boundedness and passivity for uncertainties are proposed by employing zero inequalities. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.

Global Asymptotic Stability and Stabilization of Neural Networks With General Noise

Neural networks (NNs) in the stochastic environment were widely modeled as stochastic differential equations, which were driven by white noise, such as Brown or Wiener process in the existing papers. However, they are not necessarily the best models to describe dynamic characters of NNs disturbed by nonwhite noise in some specific situations. In this paper, general noise disturbance, which may be nonwhite, is introduced to NNs. Since NNs with nonwhite noise cannot be described by Itô integral equation, a novel modeling method of stochastic NNs is utilized. By a framework in light of random field approach and Lyapunov theory, the global asymptotic stability and stabilization in probability or in the mean square of NNs with general noise are analyzed, respectively. Criteria for the concerned systems based on linear matrix inequality are proposed. Some examples are given to illustrate the effectiveness of the obtained results.

Robust Fault Estimation Design for Discrete-Time Nonlinear Systems via A Modified Fuzzy Fault Estimation Observer

The paper provides relaxed designs of fault estimation observer for nonlinear dynamical plants in the Takagi-Sugeno form. Compared with previous theoretical achievements, a modified version of fuzzy fault estimation observer is implemented with the aid of the so-called maximum-priority-based switching law. Given each activated switching status, the appropriate group of designed matrices can be provided so as to explore certain key properties of the considered plants by means of introducing a set of matrix-valued variables. Owing to the reason that more abundant information of the considered plants can be updated in due course and effectively exploited for each time instant, the conservatism of the obtained result is less than previous theoretical achievements and thus the main defect of those existing methods can be overcome to some extent in practice. Finally, comparative simulation studies on the classical nonlinear truck-trailer model are given to certify the benefits of the theoretic achievement which is obtained in our study.

Reachable Set Estimation for Markovian Jump Neural Networks With Time-Varying Delays

In this paper, the reachable set estimation problem is investigated for Markovian jump neural networks (NNs) with time-varying delays and bounded peak disturbances. Our goal is to find a set as small as possible which bounds all the state trajectories of the NNs under zero initial conditions. In the framework of Lyapunov-Krasovskii theorem, a newly-found summation inequality combined with the reciprocally convex approach is used to bound the difference of the proposed Lyapunov functional. A new less conservative condition dependent on the upper bound, the lower bound and the delay range of the time delay is established to guarantee that the state trajectories are bounded within an ellipsoid-like set. Then the result is extended to the case with incomplete transition probabilities and a more general condition is derived. Finally, examples including a genetic regulatory network are given to demonstrate the usefulness and the effectiveness of the results obtained in this paper.

Neural Network-Based Passive Filtering for Delayed Neutral-Type Semi-Markovian Jump Systems

This paper investigates the problem of exponential passive filtering for a class of stochastic neutral-type neural networks with both semi-Markovian jump parameters and mixed time delays. Our aim is to estimate the states by designing a Luenberger-type observer, such that the filter error dynamics are mean-square exponentially stable with an expected decay rate and an attenuation level. Sufficient conditions for the existence of passive filters are obtained, and a convex optimization algorithm for the filter design is given. In addition, a cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem, which can be readily solved by the existing optimization techniques. Numerical examples are given to demonstrate the effectiveness of the proposed techniques.

Mixed H-Infinity and Passive Filtering for Discrete Fuzzy Neural Networks With Stochastic Jumps and Time Delays

In this brief, the problems of the mixed H-infinity and passivity performance analysis and design are investigated for discrete time-delay neural networks with Markovian jump parameters represented by Takagi-Sugeno fuzzy model. The main purpose of this brief is to design a filter to guarantee that the augmented Markovian jump fuzzy neural networks are stable in mean-square sense and satisfy a prescribed passivity performance index by employing the Lyapunov method and the stochastic analysis technique. Applying the matrix decomposition techniques, sufficient conditions are provided for the solvability of the problems, which can be formulated in terms of linear matrix inequalities. A numerical example is also presented to illustrate the effectiveness of the proposed techniques.

Observer-based robust finite time H∞ sliding mode control for Markovian switching systems with mode-dependent time-varying delay and incomplete transition rate

This paper investigates the problem of robust finite time H∞ sliding mode control for a class of Markovian switching systems. The system is subjected to the mode-dependent time-varying delay, partly unknown transition rate and unmeasurable state. The main difficulty is that, a sliding mode surface cannot be designed based on the unknown transition rate and unmeasurable state directly. To overcome this obstacle, the set of modes is firstly divided into two subsets standing for known transition rate subset and unknown one, based on which a state observer is established. A component robust finite-time sliding mode controller is also designed to cope with the effect of partially unknown transition rate. It is illustrated that the reachability, finite-time stability, finite-time boundedness, finite-time H∞ state feedback stabilization of sliding mode dynamics can be ensured despite the unknown transition rate. Finally, the simulation results verify the effectiveness of robust finite time control problem.

Synchronization of Asynchronous Switched Boolean Network

In this paper, the complete synchronizations for asynchronous switched Boolean network with free Boolean sequence controllers and close-loop controllers are studied. First, the basic asynchronous switched Boolean network model is provided. With the method of semi-tensor product, the Boolean dynamics is translated into linear representation. Second, necessary and sufficient conditions for ASBN synchronization with free Boolean sequence control and close-loop control are derived, respectively. Third, some illustrative examples are provided to show the efficiency of the proposed methods.