Markovian Jumping Neural Networks Research Articles

Synchronization of Markov Jump Neural Networks With Communication Constraints via Asynchronous Output Feedback Control.

This article is concerned with the synchronization issue of discrete Markov jump neural networks (MJNNs). First, to save communication resources, a universal communication model, including event-triggered transmission, logarithmic quantization, and asynchronous phenomenon, is proposed, which is close to the actual situation. Here, to further reduce conservatism, a more general event-triggered protocol is constructed by developing the threshold parameter as a diagonal matrix. To cope with mode mismatch between the nodes and controllers due to potentially occurring time lag and packet dropouts, a hidden Markov model (HMM) method is adopted. Second, considering that state information of nodes may not be available, the asynchronous output feedback controllers are devised by a novel decoupling strategy. Then, sufficient conditions based on linear matrix inequalities (LMIs) for dissipative synchronization of MJNNs are proposed with the virtue of Lyapunov techniques. Third, by eliminating asynchronous terms, a corollary with less computational cost is devised. Finally, two numerical examples verify the effectiveness of the above results.

Resilient Synchronization for Insecure Markovian Jump Neural Networks to Mitigate Dual Cyber Attacks

Resilient Synchronization for Insecure Markovian Jump Neural Networks to Mitigate Dual Cyber Attacks

Asynchronous adaptive event-triggered fault detection for delayed Markov jump neural networks: A delay-variation-dependent approach

This paper presents a delay-variation-dependent approach to fault detection of a discrete-time Markov jump neural network (MJNN) with a time-varying delay and mismatched modes. The goal is to detect the potential fault of delayed MJNNs by constructing an appropriate adaptive event-triggered and asynchronous H∞ filter. By choosing a delay-product-type Lyapunov–Krasovskii (L–K) functional with a delay-dependent matrix and exploiting some matrix polynomial inequalities, bounded real lemmas (BRLs) are obtained on the existence of suitable adaptive event generator and filters. These BRLs are dependent not only on the delay bounds but also on the delay variation rate. Simulation results are given to show the validity of the proposed theoretical method.

Asynchronous sampled-data dynamic output feedback control for Markovian jump neural networks via a double-mode-dependent Lyapunov functional

This paper discusses the asynchronous switching problem of Markovian jump neural networks (MJNNs) with mode-dependent time delays. Due to the factors such as communication induced phenomena or the incomplete availability of system modes, asynchronous switching between the system mode and the controller mode is a common phenomenon. Therefore considering the mode mismatch phenomenon and the incomplete measurement of system state, we propose an asynchronous dynamic output feedback control (DOFC) law. Unlike the traditional DOFC, the sampled-data strategy is introduced into DOFC to alleviate the burden of the communication network. In light of the sampled-data DOFC, an augmented dynamic system is modeled. To fully employ the mode information of asynchronous switching and to relax the conservativeness of the results, a double-mode-dependent Lyapunov functional is constructed, which depends both on the system modes and the DOFC modes. Then, a less conservative stability condition is obtained to guarantee mean-square asymptotic stability (MSAS) of the augmented system. On the basis of the stability condition, a design algorithm is attained to solve the gain matrices of the asynchronous DOFC. Finally, a simulation example is given to illustrate the validity and superiority of the developed results.

Resilient adaptive event‐triggered synchronization control of piecewise‐homogeneous Markov jump delayed neural networks under aperiodic DoS attacks

SummaryUnder the aperiodic Denial‐of‐service (DoS) attacks, this paper studies the resilient adaptive event‐triggered synchronization control problem for a class of Piecewise‐Homogeneous Uncertain Markov Jump Neural Networks (PHUMJNNs) with time‐varying delays. First of all, a new way of carving DoS attacks is given from the defenders' perspective, that is, aperiodic DoS attacks based on fixed detection periods. Then, under such attacks, a new Resilient Adaptive Event‐triggered Communication (RAETC) is designed between sensor and controller, which has a threshold function based on the net change rate and is real‐time updated depending on the present sampling state. Next, a single functional is used in the construction of the Lyapunov‐Krasovskii functional, while a new looped functional is introduced that makes full use of the state information of the current instant , the trigger instant and the next trigger instant . Based on the constructed single functional, under the framework of the input delay method and the linear matrix inequality technique, the exponential mean square stabilization criterion of the error system is obtained, which makes the master system and the slave system synchronized. In the end, three simulation examples are used to illustrate the validity of the obtained results.

Security control of Markovian jump neural networks with stochastic sampling subject to false data injection attacks★ ★This work was supported by the NNSF of China under Grants 61973199, 62003794, 62173214, the Shandong Provincial NSF ZR2020QF050, ZR2021MF003.

The security control of Markovian jumping neural networks (MJNNs) is investigated under false data injection attacks that take place in the shared communication network. Stochastic sampled-data control is employed to research the exponential synchronization of MJNNs under false data injection attacks (FDIAs) since it can alleviate the impact of the FDIAs on the performance of the system by adjusting the sampling periods. A multi-delay error system model is established through the input-delay approach. To reduce the conservatism of the results, a sampling-period-probability-dependent looped Lyapunov functional is constructed. In light of some less conservative integral inequalities, a synchronization criterion is derived, and an algorithm is provided that can be solved for determining the controller gain. Finally, a numerical simulation is presented to confirm the efficiency of the proposed method.

Reachable set estimation and stochastic sampled-data exponential synchronization of Markovian jump neural networks with time-varying delays

In this paper, the stochastic sampled-data exponential synchronization problem for Markovian jump neural networks (MJNNs) with time-varying delays and the reachable set estimation (RSE) problem for MJNNs subjected to external disturbances are investigated. Firstly, assuming that two sampled-data periods satisfy Bernoulli distribution, and introducing two stochastic variables to represent the unknown input delay and the sampled-data period respectively, the mode-dependent two-sided loop-based Lyapunov functional (TSLBLF) is constructed, and the conditions for the mean square exponential stability of the error system are derived. Furthermore, a mode-dependent stochastic sampled-data controller is designed. Secondly, by analyzing the unit-energy bounded disturbance of MJNNs, a sufficient condition is proved that all states of MJNNs are confined to an ellipsoid under zero initial condition. In order to make the target ellipsoid contain the reachable set of the system, a stochastic sampled-data controller with RSE is designed. Eventually, two numerical examples and an analog resistor–capacitor network circuit are provided to show that the textual approach can obtain a larger sampled-data period than the existing approach.

Stochastic Sampled-Data Exponential Synchronization of Markovian Jump Neural Networks With Time-Varying Delays.

In this article, the exponential synchronization of Markovian jump neural networks (MJNNs) with time-varying delays is investigated via stochastic sampling and looped-functional (LF) approach. For simplicity, it is assumed that there exist two sampling periods, which satisfies the Bernoulli distribution. To model the synchronization error system, two random variables that, respectively, describe the location of the input delays and the sampling periods are introduced. In order to reduce the conservativeness, a time-dependent looped-functional (TDLF) is designed, which takes full advantage of the available information of the sampling pattern. The Gronwall-Bellman inequalities and the discrete-time Lyapunov stability theory are utilized jointly to analyze the mean-square exponential stability of the error system. A less conservative exponential synchronization criterion is derived, based on which a mode-independent stochastic sampled-data controller (SSDC) is designed. Finally, the effectiveness of the proposed control strategy is demonstrated by a numerical example.

Memory-based adaptive event-triggered secure control of Markovian jumping neural networks suffering from deception attacks

Memory-based adaptive event-triggered secure control of Markovian jumping neural networks suffering from deception attacks

Dynamic Event-Triggered State Estimation for Markov Jump Neural Networks With Partially Unknown Probabilities.

This article focuses on the investigation of finite-time dissipative state estimation for Markov jump neural networks. First, in view of the subsistent phenomenon that the state estimator cannot capture the system modes synchronously, the hidden Markov model with partly unknown probabilities is introduced in this article to describe such asynchronization constraint. For the upper limit of network bandwidth and computing resources, a novel dynamic event-triggered transmission mechanism, whose threshold parameter is constructed as an adjustable diagonal matrix, is set between the estimator and the original system to avoid data collision and save energy. Then, with the assistance of Lyapunov techniques, an event-based asynchronous state estimator is designed to ensure that the resulting system is finite-time bounded with a prescribed dissipation performance index. Ultimately, the effectiveness of the proposed estimator design approach combining with a dynamic event-triggered transmission mechanism is demonstrated by a numerical example.

Sampled-data control for synchronization of Markovian jumping neural networks with packet dropout

Sampled-data control for synchronization of Markovian jumping neural networks with packet dropout

Reachable Set Estimation of Delayed Markovian Jump Neural Networks Based on an Improved Reciprocally Convex Inequality.

This brief investigates the reachable set estimation problem of the delayed Markovian jump neural networks (NNs) with bounded disturbances. First, an improved reciprocally convex inequality is proposed, which contains some existing ones as its special cases. Second, an augmented Lyapunov-Krasovskii functional (LKF) tailored for delayed Markovian jump NNs is proposed. Thirdly, based on the proposed reciprocally convex inequality and the augmented LKF, an accurate ellipsoidal description of the reachable set for delayed Markovian jump NNs is obtained. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

Event-Triggered [formula omitted]-state estimation for Markovian jumping neural networks with mixed time-delays

In this paper, the issue of event-triggered μ-state estimation is addressed for a class of Markovian jumping neural networks (MJNNs) with mixed delays. The mixed delays involve both the infinitely distributed delay and the time-varying delay without requiring the upper bound, which has a distinction in existing conclusions and makes the model be more comprehensive. An event-triggered mechanism (ETM) with mode dependence is adopted to determine the appropriate updating instants of measurement outputs so as to alleviate the transmission of signals. By constructing a novel time-varying L-K functional with a general convergency rate and employing several analysis techniques, a sufficient criterion is obtained for ensuring the stochastic μ-stability performance of error system, which is a more general stability performance including exponential stability, power stability as well as logarithmic stability as its special cases. Finally, three numerical examples are listed to demonstrate the effectiveness of the proposed method.

Asynchronous H∞ Dynamic Output Feedback Control for Markovian Jump Neural Networks with Time-varying Delays

Asynchronous H∞ Dynamic Output Feedback Control for Markovian Jump Neural Networks with Time-varying Delays

Extended Dissipative Criteria for Generalized Markovian Jump Neural Networks Including Asynchronous Mode-Dependent Delayed States

Extended Dissipative Criteria for Generalized Markovian Jump Neural Networks Including Asynchronous Mode-Dependent Delayed States

A New Free-matrix Inequality with application to Exponential State Estimation for Markov Jump Neural Networks

This paper is concerned with an exponential state estimation problem for a class of Markov Jump Neural Networks (MJNNs) with Time-varying Delay (TVD). Firstly, to derive a tighter bound of Exponential-type Integral Quadratic Terms (EIQTs), a new Free-matrix Exponential-type Inequality (FMEI) is provided, which includes some existing ones as its special cases. Secondly, by fully considering the information of attenuation exponent and TVD, a novel Lyapunov-Krasovskii Functional (LKF) is constructed. Then, by employing the new FMEI and other analytical techniques, a less conservative criterion guaranteeing the stochastic stability of the error system is obtained in form of Linear Matrix Inequalities (LMIs). In the end, a numerical example is given to show the effectiveness of the obtained result.

Stochastic stability and extended dissipativity analysis for delayed neural networks with markovian jump via novel integral inequality

This paper studies the stochastic stability and extended dissipativity analysis for delayed Markovian jump neural networks (MJNNs) with partly unknown transition rates (PUTRs) using novel integral inequality. A new double integral inequality with augmented vector is introduced through inequality technique and the zero-valued equality approach, which can more efficiently estimate the derivative of the triple integral inequality. Next, an augmented Lyapunov-Krasovskii functional (LKF) with delay-product-type (DPT) is constructed. Besides, with the introduced integral inequality, the augmented LKF and some other analytical techniques, some less conservative extended dissipation conditions are obtained in the form of linear matrix inequality (LMI). Finally, several examples are provided to illustrate the effectiveness of the obtained results.

Sampled-data synchronization criteria for Markovian jumping neural networks with additive time-varying delays using new techniques

This paper investigates the sampled-data synchronization issue of Markovian jumping neural networks with additive time-varying delays. Firstly, a ternary quadratic function negative-determination condition and the bilateral sampled-interval-related Lyapunov functional (BSIRLF) approach are proposed. Based on the developed two novel approaches, some new criteria based on the linear matrix inequalities (LMIs) are established to guarantee the drive-response stochastic sampled-data synchronization of Markovian jumping neural networks with additive time-varying delays. Meanwhile, the corresponding sampled-data controller gains are designed under the larger sampling interval. In the end, the availability and merits of the developed approaches are displayed via two simulative examples.

Formula omitted] performance analysis for delayed Markovian jump neural networks via the Lyapunov-Krasovskii functional with delay-product-type terms

This paper studies the problem of H∞ performance analysis for delayed Markovian jump neural networks (MJNNs). Firstly, the third-order Bessel–Legendre (B-L) integral inequality based on reciprocally convex approach is derived, which contains some existing ones as its special cases. Secondly, in order to facilitate the use of more information about time delays, the Lyapunov–Krasovskii functional (LKF) with delay-product-type terms is proposed. As a result, by utilizing the LKF with delay-product-type terms and the third-order B-L integral inequality based on reciprocally convex approach, less conservative sufficient conditions that guarantee the H∞ performance for delayed MJNNs are obtained. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

Finite-Time H ∞ State Estimation for Markovian Jump Neural Networks with Time-Varying Delays via an Extended Wirtinger’s Integral Inequality

This study investigates the finite-time boundedness for Markovian jump neural networks (MJNNs) with time-varying delays. An MJNN consists of a limited number of jumping modes wherein it can jump starting with one mode then onto the next by following a Markovian process with known transition probabilities. By constructing new Lyapunov–Krasovskii functional (LKF) candidates, extended Wirtinger’s, and Wirtinger’s double inequality with multiple integral terms and using activation function conditions, several sufficient conditions for Markovian jumping neural networks are derived. Furthermore, delay-dependent adequate conditions on guaranteeing the closed-loop system which are stochastically finite-time bounded (SFTB) with the prescribed H ∞ performance level are proposed. Linear matrix inequalities are utilized to obtain analysis results. The purpose is to obtain less conservative conditions on finite-time H ∞ performance for Markovian jump neural networks with time-varying delay. Eventually, simulation examples are provided to illustrate the validity of the addressed method.