Bernoulli Stochastic Variables Research Articles

Practical Fixed-Time Bipartite Synchronization of Uncertain Coupled Neural Networks Subject to Deception Attacks via Dual-Channel Event-Triggered Control.

This article investigates the practical fixed-time synchronization of uncertain coupled neural networks via dual-channel event-triggered control. Contrary to some previous studies, the bipartite synchronization of signed graphs representing cooperative and antagonistic interactions is studied. The communication channel is introduced into deception attacks, which are described by Bernoulli's stochastic variables. Based on the concept of two channels, event-triggered mechanisms are designed for sensor-to-controller and controller-to-actuator channels to reduce communication consumption and controller update consumption as much as possible. Lyapunov and comparison theories are used to derive synchronization criteria and explicit expression of settling time. An example of Chua's circuit system is presented to demonstrate the feasibility of the obtained theoretical results.

Event-triggered H∞ control for uncertain discrete-time singular systems via sliding mode approach

This article analyzes the event-triggered (ET) scheme for uncertain discrete-time singular systems via [Formula: see text] sliding mode control (SMC). The issue of network delay is taken into account, and a Bernoulli stochastic variable is used to explain its distribution feature. A sliding mode surface (SMS) function is built by using ET scheme, and the corresponding sliding mode dynamics (SMD) is combined. Then, based on Lyapunov-Kravoskii functional (LKF) stability theory and linear matrix inequality (LMI) technology, [Formula: see text]-admissibility criterion for closed-loop SMD is deduced. Additionally, an improved SMC rule based on ET strategy is created so that the system trajectories can be driven onto the prescribed SMS in finite time. Finally, the effectiveness of the approach is demonstrated by three simulated examples.

Mean-square bounded synchronization of fractional-order chaotic Lur’e systems under deception attack

This paper discussed the mean-square bounded synchronization (MSBS) of fractional-order chaotic Lur’e systems (FOCLSs) in the presence of deception attacks. Firstly, it was assumed that the channel of the controller to the actuator was subjected to stochastic deception attacks, which were modeled by the Bernoulli stochastic variable. Secondly, impulsive control was proposed to achieve the aim of the MSBS of FOCLSs. Moreover, the event-triggered mechanism (ETM) is added to the impulsive control to decrease the controller update times and save computing resources consumption. Applied the fractional-order calculus, the Laplace transform, and the definition of MSBS, sufficient criteria were derived to guarantee the MSBS of FOCLSs, with the criteria being dependent on the order of the system. The upper bound of the synchronization error is given for the error system under impulsive control and event-triggered impulsive control (ETIC), respectively. Finally, Chua’s circuit was employed to indicate the practicability of the MSBS of FOCLSs.

Energy-Efficient Distributed Formation Control of Sampled-Data Multiagent Systems With Packet Losses.

This article investigates an energy-efficient formation control problem for multiagent systems with sampled data and random packet losses. A Bernoulli stochastic variable is used to describe packet losses, which is defined relative to the transmission energy consumed by antennas. A distributed sampled-data formation control law is designed and some analytic sufficient conditions on the formation control are derived. It is revealed that the sampling period, control parameters, network topology, as well as the transmission energy used by sensors impose inherent limitations in achieving the formation. Also, a method for searching the minimum allowable transmission energy is presented. Finally, numerical simulations are shown for illustration and verification.

Matrix Measure-Based Event-Triggered Impulsive Quasi-Synchronization on Coupled Neural Networks.

In this article, the quasi-synchronization for a kind of coupled neural networks with time-varying delays is investigated via a novel event-triggered impulsive control approach. In view of the randomly occurring uncertainties (ROUs) in the communication channels, the global quasi-synchronization for the coupled neural networks within a given error bound is considered instead of discussing the complete synchronization. A kind of distributed event-triggered impulsive controllers is presented with considering the Bernoulli stochastic variables based on ROUs, which works at each event-triggered impulsive instant. According to the matrix measure method and the Lyapunov stability theorem, several sufficient conditions for the realization of the quasi-synchronization are successfully derived. Combining with the mathematical methodology with the formula of variation of parameters and the comparison principle for the impulsive systems with time-varying delays, the convergence rate and the synchronization error bound are precisely estimated. Meanwhile, the Zeno behaviors could be eliminated in the coupled neural network with the proposed event-triggered function. Finally, a numerical example is presented to prove the results of theoretical analysis.

Quantized guaranteed cost dynamic output feedback control for uncertain nonlinear networked systems with external disturbance

In this article, the guaranteed cost control problem for a class of nonlinear networked control systems (NCSs) with dynamic quantization, external bounded disturbance, and data dropout is investigated via the dynamic output feedback. The Takagi–Sugeno (T-S) fuzzy model is used to represent the discrete-time nonlinear system discussed in this paper. Under the dynamic quantization strategy, two quantizers with dynamic parameters are used to quantize the measured output and control input, and the data dropout process is described by introducing the Bernoulli stochastic variable. By using the quadratic boundedness technique, the quadratic stability of the quantized NCS with external disturbance is described. Furthermore, the sufficient condition for the global design approach are proposed, that is, not only the dynamic output feedback controller but parameters of the quantizers are designed synchronously with strict linear matrix inequalities. Eventually, a simulation of nonlinear mass-spring-damper mechanical system is carried out to verify the effectiveness of the provided algorithm.

Proportional-Integral Observer-Based State Estimation for Singularly Perturbed Complex Networks With Cyberattacks.

This article investigates the asynchronous proportional-integral observer (PIO) design issue for singularly perturbed complex networks (SPCNs) subject to cyberattacks. The switching topology of SPCNs is regulated by a nonhomogeneous Markov switching process, whose time-varying transition probabilities are polytope structured. Besides, the multiple scalar Winner processes are applied to character the stochastic disturbances of the inner linking strengths. Two mutually independent Bernoulli stochastic variables are exploited to characterize the random occurrences of cyberattacks. In a practical viewpoint, by resorting to the hidden nonhomogeneous Markov model, an asynchronous PIO is formulated. Under such a framework, by applying the Lyapunov theory, sufficient conditions are established such that the augmented dynamic is mean-square exponentially ultimately bounded. Finally, the effectiveness of the theoretical results is verified by two numerical simulations.

An outlier‐resistant approach to observer‐based security control for interval type‐2 T‐S fuzzy systems subject to deception attacks

This article focuses on the outlier-resistant observer-based controller for the interval type-2 T-S fuzzy discrete-time systems with distributed delays under deception attacks. The deception attack takes place between sensor channel and observer channel. A neoteric guidance for safety performance is constructed to explain the randomly happening spoofing offensive on the control structure. The random events of parameter uncertainty and spoofing offensives are controlled via two sets of Bernoulli stochastic variables with foregone probability distributions. One outlier-resistant observer-based security control is constructed to induce an innovation saturation structure in order to alleviate the passive influence on the spoofing offensives about the estimation aspect. The goal of the solution is to design an outlier-resistant observer-based security control that can insure boundedness in estimation error while achieving the ideal level of safety. Ultimately, a quantitative value simulation sample is put forward to justify the practicality and validity of the above-mentioned control project.

Adaptive Event‐Triggered Control for Complex Dynamical Network with Random Coupling Delay under Stochastic Deception Attacks

This study concentrates on adaptive event‐triggered control of complex dynamical networks with unpredictable coupling delays and stochastic deception attacks. The adaptive event‐triggered mechanism is used to avoid the wasting of limited bandwidth. The probability of data communicated by the network is established by statistical properties and Bernoulli stochastic variables with an uncertain occurrence probability. Stability analysis based on Lyapunov–Krasovskii functional (LKF) and the stability of the closed‐loop system is guaranteed. Using the LMI technique, we obtain triggered parameters. To demonstrate the feasibility and usefulness of the suggested methodology, two examples are shown.

Fixed-time dual-channel event-triggered secure quasi-synchronization of coupled memristive neural networks

This paper is concerned with the fixed-time quasi-synchronization of coupled memristive neural networks (CMNNs). The communication channel is subject to the deception attack described by the Bernoulli stochastic variable. To reduce signal transmissions, a dual-channel event-triggered mechanism is proposed. In each channel of sensor to controller and controller to actuator, an event-triggered mechanism is designed. Compared with the single event-triggered mechanism in the communication loop, the main difficulties lie in how to deal with the problems of packet scheduling and network attacks. By using Lyapunov method combining with a new proposed lemma, some sufficient conditions are derived to guarantee the leader-following quasi-synchronization of CMNNs. The Zeno behavior is excluded for the designed dual-channel event-triggered mechanism. The influence of the event-triggered mechanism on the estimation of settling time is discussed. Three numerical examples are provided to show the effectiveness of the theoretical results.

Secure synchronization of complex networks under deception attacks against vulnerable nodes

Secure synchronization for a class of nonlinearly coupled complex networks with deception attacks is investigated in this paper. False data caused by deception attacks is assumed to be injected into both the sensor-to-controller channels and the controller-to-actuator channels, which is modelled by Bernoulli stochastic variable. A distributed controller combined with impulsive protocol is applied for realizing the secure synchronization. By jointly applying the definition of average impulsive gain, the definition of average impulsive interval and the Lyapunov stability theorem, sufficient criteria are obtained to ensure the secure synchronization within the given error bound. In addition, pinning impulsive method is proposed to describe the attacks on vulnerable systems in complex networks, therefore, the theorem is extended to a less conservative situation. Finally, two numerical examples are presented to illustrate the effectiveness of theoretical results.

Event-triggered distributed filtering for Markov jump systems over sensor networks

This article deals with the distributed filtering problem for a class of discrete-time Markov jump systems over sensor networks. First, in the distributed filtering network, each local filter simultaneously fuses the estimation and measurement from itself and neighboring nodes to achieve the system state estimation. And each sensor intelligent node is embedded with an event-triggered sampling mechanism, which can reduce the computation load or saving limited network bandwidth. Then, we use Bernoulli stochastic variables to describe whether the filtering network can successfully receive the system jump modes. Next, based on the Lyapunov stability theory, we design a distributed filter dependent on partial system modes, which has the exponential stability in mean square and [Formula: see text] performance. Finally, all desired estimator parameters can be obtained by solving a set of linear matrix inequalities. Moreover, two numerical examples are given to illustrate the effectiveness of the distributed [Formula: see text] filtering design approach.

Distributed Synchronization of Coupled Time-Delay Neural Networks Based on Randomly Occurring Control

In this paper, the distributed synchronization of stochastic coupled neural networks with time-varying delay is concerned via randomly occurring control. We use two Bernoulli stochastic variables to describe the occurrence of distributed adaptive control and updating law according to certain probabilities. The distributed adaptive control and updating law for each vertex in the network depend on the state information on each vertex’s neighborhood. Based on Lyapunov stability theory, It&#244 differential equations, etc., by constructing the appropriate Lyapunov functional, we study and obtain sufficient conditions for the distributed synchronization of such networks in mean square.

Sampled-data scaled group consensus for second-order multi-agent systems with switching topologies and random link failures

This article studies the sampled-data scaled group consensus problem for second-order multi-agent systems with switching topologies and random link failures. It is assumed that each agent only interacts with its neighbors at discrete sampling instants rather than the complete continuous process. It is further assumed that the phenomenon of random link failures on the communication links is characterized by a Bernoulli stochastic variable. By supposing that each agent has a unique scale, a distributed control protocol that uses the sampled position information of the neighbors is designed. With the assistance of hybrid tools including graph theory and matrix theory, a sufficient condition based on the structures of topologies, the time-varying sampling periods, and the gain parameter, is established to ensure the asymptotic convergence of the agents under the action of sampled distributed protocol. Finally, some simulation instances are provided to verify our theoretical finding.

Novel mixed-triggered filter design for interval type-2 fuzzy nonlinear Markovian jump systems with randomly occurring packet dropouts

This paper is aimed at investigating the problem of mixed-triggered filter design for interval type-2 (IT2) fuzzy nonlinear Markovian jump systems (MJSs) with randomly occurring packet dropouts. First, an IT2 fuzzy nonlinear MJSs model with parameter uncertainties is established by using IT2 fuzzy model, and the fuzzy filter is designed with different premise variables. Second, a novel mixed-triggered scheme is addressed, which can reduce the needless waste of network resources. Then, two Bernoulli stochastic variables are employed, one to randomly switch the different modes of the mixed-triggered scheme, the other to describe the randomly occurring packet dropouts. Next, in order to ensure that IT2 fuzzy filtering error system is asymptotically stable, sufficient conditions are presented. Moreover, the existence conditions for the fuzzy filter are given by the linear matrix inequalities. Finally, simulation results are given to verify the validity of the proposed method.

Cooperative containment for second-order multi-agent systems with asynchronous setting and random link failures

The issue of cooperative containment control in second-order multi-agent systems with asynchronous setting and random link failures is examined in this paper. Asynchronous setting implies that each agent uses its neighbors’ information to update the state independently at certain discrete instants. The phenomenon of random link failure on each communication link is characterized by a Bernoulli stochastic variable. An asynchronous distributed protocol is designed by randomly measuring the position information of the previous one or two steps of the neighbors. Matrix theory and the composition of binary relation are explored to handle the containment control problem with both asynchronous setting and random link failures. Under a loose parameter selection strategy, a necessary and sufficient condition in terms of the topology structure can be established. A numerical example is finally provided to validate the theoretical result.

Delay-distribution-dependent non-fragile state estimation for discrete-time neural networks under event-triggered mechanism

In this paper, the event-triggered non-fragile state estimation problem is considered for a class of uncertain discrete-time neural networks with random delays and state-dependent stochastic disturbances. The norm-bounded uncertainty goes into all the parameters of the addressed neural network model. A Bernoulli stochastic variable is introduced to characterize the probability distribution of the occurrence of the time delays. The phenomenon of estimator gain variations is considered to account for the potential implementation error of the state estimator. An event-triggered mechanism is proposed with hope to mitigate the network load and orchestrate the bandwidth utilization. We aim to design a non-fragile state estimator such that the error dynamics of the neuron state estimation is globally asymptotically stable in the mean square. By means of the Lyapunov stability theory, delay-distribution-dependent sufficient conditions are established to ensure the existence of the desired event-triggered non-fragile state estimators and the estimator parameters are then derived in terms of the solution to a set of linear matrix inequalities. An illustrative example is utilized to show the usefulness and applicability of the proposed algorithm.

Synchronization of Nonlinearly and Stochastically Coupled Markovian Switching Networks via Event-Triggered Sampling.

This paper studies the exponential synchronization problem for a new array of nonlinearly and stochastically coupled networks via events-triggered sampling (ETS) by self-adaptive learning. The networks include the following features: 1) a Bernoulli stochastic variable is introduced to describe the random structural coupling; 2) a stochastic variable with positive mean is used to model the coupling strength; and 3) a continuous time homogeneous Markov chain is employed to characterize the dynamical switching of the coupling structure and pinned node sets. The proposed network model is capable to capture various stochastic effect of an external environment during the network operations. In order to reduce networks' workload, different ETS strategies for network self-adaptive learning are proposed under continuous and discrete monitoring, respectively. Based on these ETS approaches, several sufficient conditions for synchronization are derived by employing stochastic Lyapunov-Krasovskii functions, the properties of stochastic processes, and some linear matrix inequalities. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results and the superiority of the proposed ETS approach.

Novel approaches to pin cluster synchronization on complex dynamical networks in Lur’e forms

This paper investigates the cluster synchronization of complex dynamical networks consisted of identical or nonidentical Lur’e systems. Due to the special topology structure of the complex networks and the existence of stochastic perturbations, a kind of randomly occurring pinning controller is designed which not only synchronizes all Lur’e systems in the same cluster but also decreases the negative influence among different clusters. Firstly, based on an extended integral inequality, the convex combination theorem and S-procedure, the conditions for cluster synchronization of identical Lur’e networks are derived in a convex domain. Secondly, randomly occurring adaptive pinning controllers with two independent Bernoulli stochastic variables are designed and then sufficient conditions are obtained for the cluster synchronization on complex networks consisted of nonidentical Lur’e systems. In addition, suitable control gains for successful cluster synchronization of nonidentical Lur’e networks are acquired by designing some adaptive updating laws. Finally, we present two numerical examples to demonstrate the validity of the control scheme and the theoretical analysis.

Finite-time stability of neutral-type neural networks with random time-varying delays

ABSTRACTThis paper is devoted to the finite-time stability analysis of neutral-type neural networks with random time-varying delays. The randomly time-varying delays are characterised by Bernoulli stochastic variable. This result can be extended to analysis and design for neutral-type neural networks with random time-varying delays. On the basis of this paper, we constructed suitable Lyapunov–Krasovskii functional together and established a set of sufficient linear matrix inequalities approach to guarantee the finite-time stability of the system concerned. By employing the Jensen's inequality, free-weighting matrix method and Wirtinger's double integral inequality, the proposed conditions are derived and two numerical examples are addressed for the effectiveness of the developed techniques.