Resilient fixed-time stabilization of switched neural networks subjected to impulsive deception attacks

This article focuses on the resilient fixed-time stabilization of switched neural networks (SNNs) under impulsive deception attacks. A novel theorem for the fixed-time stability of impulsive systems is established by virtue of the comparison principle. Existing fixed-time stability theorems for impulsive systems assume that the impulsive strength is not greater than 1, while the proposed theorem removes this assumption. SNNs subjected to impulsive deception attacks are modeled as impulsive systems. Some sufficient criteria are derived to ensure the stabilization of SNNs in fixed time. The estimation of the upper bound for the settling time is also given. The influence of impulsive attacks on the convergence time is discussed. A numerical example and an application to Chua's circuit system are given to demonstrate the effectiveness of the theoretical results.

Finite-Time H∞ Estimator Design for Switched Discrete-Time Delayed Neural Networks With Event-Triggered Strategy

This article is concerned with the event-triggered finite-time H_∞ estimator design for a class of discrete-time switched neural networks (SNNs) with mixed time delays and packet dropouts. To further reduce the data transmission, both the measured information of system outputs and switching signal of the SNNs are only allowed to be accessible for the constructed estimator at the certain triggering time instants. Under this consideration, the simultaneous presence of the switching and triggering actions also leads to the asynchronism between the indices of the SNNs and the designed estimator. Unlike the existing event-triggered strategies for the general switched linear systems, the proposed event-triggered mechanism not only allows the occurrence of multiple switches in one triggering interval but also removes the minimum dwell-time constraint on the switched signal. In light of the piecewise Lyapunov-Krasovskii functional theory, sufficient conditions are developed for the estimation error system to be stochastically finite-time bounded with a finite-time specified H_∞ performance. Finally, the effectiveness and applicability of the theoretical results are verified by a switched Hopfield neural network.

l₂-l∞ State Estimation for Persistent Dwell-Time Switched Coupled Networks Subject to Round-Robin Protocol

This article is concerned with the issue of l₂ - l_∞ state estimation for nonlinear coupled networks, where the variation of coupling mode is governed by a set of switching signals satisfying a persistent dwell-time property. To solve the problem of data collisions in a constrained communication network, the round-robin protocol, as an important scheduling strategy for orchestrating the transmission order of sensor nodes, is introduced. Redundant channels with signal quantization are used to improve the reliability of data transmission. The main purpose is to determine an estimator that can guarantee the exponential stability in mean square sense and an l₂ - l_∞ performance level of the estimation error system. Based on the Lyapunov method, sufficient conditions for the addressed problem are established. The desired estimator gains can be obtained by addressing a convex optimization case. The correctness and availability of the developed approach are finally explained via two illustrative examples.

Sampled-Data-Based H∞ Synchronization of Switched Coupled Neural Networks

This paper investigates the sampled-data-based H_∞ synchronization problem for a class of switched coupled neural networks subject to exogenous perturbations. Different from the existing results on the nonswitched and continuous-time control cases, the unmatched phenomena between the switching of the system models and that of the controllers will occur, when the resulting error system switches within a sampling interval. In the framework of time-dependent switching mechanism, sufficient conditions for the existence of the sampled-data controllers are derived under the variable sampling and asynchronous switching. We prove that the proposed method not only renders the synchronization error system exponentially stable but also constrains the influence of the exogenous perturbations on the synchronization performance at a specified level. Finally, a switched coupled cellular neural network and a switched coupled Hopfield neural network are provided to illustrate the applicability and validity of the developed results.

Design of State-Dependent Switching Laws for Stability of Switched Stochastic Neural Networks With Time-Delays

We study the stability properties of switched stochastic neural networks (SSNNs) with time-varying delays whose subsystem is not necessarily stable. We introduce state-dependent switching (SDS) as a tool for stability analysis. Some SDS laws for asymptotic stability and p th moment exponentially stable are designed by employing Lyapunov-Krasovskii (L-K) functional and Lyapunov-Razumikhin (L-R) method, respectively. It is shown that the stability of SSNNs with time-varying delays composed of unstable subsystems can be achieved by using SDS law. The control gains in the designed SDS laws can be derived by solving the LMIs in derived stability criteria. Two numerical examples are provided to demonstrate the effectiveness of the proposed SDS laws.

Estimation of Domain of Attraction for Aperiodic Sampled-Data Switched Delayed Neural Networks Subject to Actuator Saturation

In this paper, for the case of the asynchronous switching caused by that subsystem's switching occuring during a sampling interval, the domain of attraction estimation problem is investigated for aperiodic sampled-data switched delayed neural networks (ASDSDNNs) subject to actuator saturation. A parameters-dependent time-scheduled Lyapunov functional consisting of a novel looped-functional is constructed using segmentation technology and linear interpolation. By employing this novel functional and using an average dwell time (ADT) approach, exponential stability criteria are proposed for polytopic uncertain ASDSDNNs subject to actuator saturation. And a relationship between ADT and sampling period is revealed for ASDSDNNs. As a corollary, exponential stability criteria are proposed for nominal ASDSDNNs subject to actuator saturation. Furthermore, by describing the domain of attraction as a time-varying ellipsoid determined by the time-scheduled Lyapunov matrix, the proposed theoretical conditions are transformed into a linear matrix inequality (LMI)-based multi-objective optimization problem. The dynamic estimates of the domain of attraction for ASDSDNNs are solved. Numerical simulation examples are provided to illustrate the effectiveness of the proposed method.

Region Stabilization of Switched Neural Networks With Multiple Modes and Multiple Equilibria: A Pole Assignment Method

This article investigates region stabilization issue of switched neural networks (SNNs) with multiple modes (MMs) and multiple equilibria (ME) via a pole assignment method. In such an SNN, every neuron is observed with more than one mode and unstable equilibrium point. First, SNNs with MMs and ME are modeled in terms of switched systems with unstable subsystems and ME. Second, a necessary and sufficient condition and a sufficient condition are, respectively, proposed for arbitrary switching paths pole assignment and arbitrary periodic/quasi-periodic switching paths (PSPs/QSPs) asymptotically region stabilizing pole assignment of switched linear time-invariant (LTI) systems with ME. It is shown that to stabilize a switched LTI system, some/all poles of all/some linear subsystems can be assigned to suitable locations of the right-half side of the complex plane. Third, based on the obtained pole assignment results, an asymptotical-region-stabilizing-control law observed as distributed state feedback controllers of MMs, asymptotical-region-stabilizing PSPs/QSPs, and a corresponding algorithm are all designed for asymptotical region stabilization of switched linear/nonlinear neural networks with MMs and ME. Finally, a numeral example is given to illustrate the effectiveness and practicality of the new results.

Optimized Neural Network Parameters Using Stochastic Fractal Technique to Compensate Kalman Filter for Power System-Tracking-State Estimation

Tracking-state estimation uses previous state vector and recent measurement data to give real-time update on the state of the power system noniteratively during the subsequent time sampling. This paper discusses Kalman filtering enhanced by optimized neural network parameters-based stochastic fractals search technique (KF-MLP-based SFS). Both KF gain (mismodeling error) and measurement noise were replaced by optimized multilayer perceptron (MLP-SFS). This optimized MLP-based SFS could suppress filter divergence and improve the accuracy. The proposed method was used to detect and identify anomalies exhibited in normal operation where loads fluctuate linearly, bad data condition, sudden loss of loads, generators, and transmission lines. The application of the proposed technique (KF-MLP-based SFS) is illustrated on the IEEE 57-bus system. Results of the presented approach are compared to the true state vector (load flow), KF standalone, and KF compensated by radial basis function.

Protocol-based state estimation for delayed Markovian jumping neural networks

This paper is concerned with the state estimation problem for a class of Markovian jumping neural networks (MJNNs) with sensor nonlinearities, mode-dependent time delays and stochastic disturbances subject to the Round-Robin (RR) scheduling mechanism. The system parameters experience switches among finite modes according to a Markov chain. As an equal allocation scheme, the RR communication protocol is introduced for efficient usage of limited bandwidth and energy saving. The update matrix method is adopted to deal with the periodic time-delays resulting from the RR protocol. The objective of the addressed problem is to construct a state estimator for the MJNNs such that the dynamics of the estimation error is exponentially ultimately bounded in the mean square with a certain upper bound. Sufficient conditions are established for the existence of the desired state estimator by resorting to a combination of the Lyapunov stability theory and the stochastic analysis technique. Furthermore, the estimator gain matrices are characterized in terms of the solution to a convex optimization problem. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed estimator design strategy.

Stability Analysis of Genetic Regulatory Networks With Switching Parameters and Time Delays

This paper is concerned with the exponential stability analysis of genetic regulatory networks (GRNs) with switching parameters and time delays. In this paper, a new integral inequality and an improved reciprocally convex combination inequality are considered. By using the average dwell time approach together with a novel Lyapunov-Krasovskii functional, we derived some conditions to ensure the switched GRNs with switching parameters and time delays are exponentially stable. Finally, we give two numerical examples to clarify that our derived results are effective.

A New Result on $H_{\infty }$ State Estimation of Delayed Static Neural Networks

This brief presents a new guaranteed performance state estimation criterion for delayed static neural networks. To facilitate the use of the slope information about activation function, the estimation error of activation function is separated into two parts for the first time. Then, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which has fully captured the slope information of the activation. Based on the new LKF, a less conservative design criterion of estimator is derived to ensure the asymptotic stability of estimation error system with performance. The desired estimator gain matrices and the performance index are obtained by solving a convex optimization problem. The simulation results show that the proposed method has much better performance than the most recent results.

Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays

This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.

On Stabilization of Quantized Sampled-Data Neural-Network-Based Control Systems

This paper investigates the problem of stabilization of sampled-data neural-network-based systems with state quantization. Different with previous works, the communication limitation of state quantization is considered for the first time. More specifically, it is assumed that the sampled state measurements from sensor to the controller are quantized via a quantizer. To reduce conservativeness, a novel piecewise Lyapunov-Krasovskii functional (LKF) is constructed by introducing a line-integral type Lyapunov function and some useful terms that take full advantage of the available information about the actual sampling pattern. Based on the new LKF, much less conservative stabilization conditions are derived to obtain the maximal sampling period and the minimal guaranteed cost control performance. The desired quantized sampled-data three-layer fully connected feedforward neural-network-based controllers are designed by a linear matrix inequality approach. A search algorithm is given to find the optimal values of tuning parameters. The effectiveness and advantage of proposed method are demonstrated by the numerical simulation of an inverted pendulum.

Filtering of Discrete-Time Switched Neural Networks Ensuring Exponential Dissipative and $l_{2}$ - $l_{\infty }$ Performances

This paper studies delay-dependent exponential dissipative and l₂ - l_∞ filtering problems for discrete-time switched neural networks (DSNNs) including time-delayed states. By introducing a novel discrete-time inequality, which is a discrete-time version of the continuous-time Wirtinger-type inequality, we establish new sets of linear matrix inequality (LMI) criteria such that discrete-time filtering error systems are exponentially stable with guaranteed performances in the exponential dissipative and l₂ - l_∞ senses. The design of the desired exponential dissipative and l₂ - l_∞ filters for DSNNs can be achieved by solving the proposed sets of LMI conditions. Via numerical simulation results, we show the validity of the desired discrete-time filter design approach.

Observer-Based Output-Feedback Asynchronous Control for Switched Fuzzy Systems

This paper investigates an output-feedback control design problem for a class of switched continuous-time Takagi-Sugeno (T-S) fuzzy systems. The considered fuzzy systems consist of several switching modes and each switching mode is described by T-S fuzzy models. In addition, there exists the asynchronous switching between the system switching modes and the controller switching modes. By using parallel distributed compensation design method, the output-feedback control schemes are developed based on state observers for the measurable and immeasurable premise variables cases. The sufficient conditions of ensuring the switched control system stabilization are proposed based on the theory of Lyapunov stability and average-dwell time methods. The controller and observer gains are obtained via two-step method. An illustrated numerical example is provided to show the effectiveness of the proposed control approaches.

Event-Triggered State Estimation for Discrete-Time Multidelayed Neural Networks With Stochastic Parameters and Incomplete Measurements

In this paper, the event-triggered state estimation problem is investigated for a class of discrete-time multidelayed neural networks with stochastic parameters and incomplete measurements. In order to cater for more realistic transmission process of the neural signals, we make the first attempt to introduce a set of stochastic variables to characterize the random fluctuations of system parameters. In the addressed neural network model, the delays among the interconnections are allowed to be different, which are more general than those in the existing literature. The incomplete information under consideration includes randomly occurring sensor saturations and quantizations. For the purpose of energy saving, an event-triggered state estimator is constructed and a sufficient condition is given under which the estimation error dynamics is exponentially ultimately bounded in the mean square. It is worth noting that the ultimate boundedness of the error dynamics is explicitly estimated. The characterization of the desired estimator gain is designed in terms of the solution to a certain matrix inequality. Finally, a numerical simulation example is presented to illustrate the effectiveness of the proposed event-triggered state estimation scheme.

Synchronization of a Class of Switched Neural Networks with Time-Varying Delays via Nonlinear Feedback Control

This paper is concerned with the synchronization problem for a class of switched neural networks (SNNs) with time-varying delays. First, a new crucial lemma which includes and extends the classical exponential stability theorem is constructed. Then by using the lemma, new algebraic criteria of ψ -type synchronization (synchronization with general decay rate) for SNNs are established via the designed nonlinear feedback control. The ψ -type synchronization which is in a general framework is obtained by introducing a ψ -type function. It contains exponential synchronization, polynomial synchronization, and other synchronization as its special cases. The results of this paper are general, and they also complement and extend some previous results. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results.

Stability analysis for uncertain switched neural networks with time-varying delay

In this paper, stability for a class of uncertain switched neural networks with time-varying delay is investigated. By exploring the mode-dependent properties of each subsystem, all the subsystems are categorized into stable and unstable ones. Based on Lyapunov-like function method and average dwell time technique, some delay-dependent sufficient conditions are derived to guarantee the exponential stability of considered uncertain switched neural networks. Compared with general results, our proposed approach distinguishes the stable and unstable subsystems rather than viewing all subsystems as being stable, thus getting less conservative criteria. Finally, two numerical examples are provided to show the validity and the advantages of the obtained results.

Exponential H∞ filtering for discrete-time switched neural networks with random delays

This paper addresses the exponential H∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays. The involved delays are assumed to be randomly time-varying which are characterized by introducing a Bernoulli stochastic variable. Effects of both variation range and distribution probability of the time delays are considered. The nonlinear activation functions are assumed to satisfy the sector conditions. Our aim is to estimate the state by designing a full order filter such that the filter error system is globally exponentially stable with an expected decay rate and a H∞ performance attenuation level. The filter is designed by using a piecewise Lyapunov-Krasovskii functional together with linear matrix inequality (LMI) approach and average dwell time method. First, a set of sufficient LMI conditions are established to guarantee the exponential mean-square stability of the augmented system and then the parameters of full-order filter are expressed in terms of solutions to a set of LMI conditions. The proposed LMI conditions can be easily solved by using standard software packages. Finally, numerical examples by means of practical problems are provided to illustrate the effectiveness of the proposed filter design.

Passivity of switched recurrent neural networks with time-varying delays

This paper is concerned with the passivity analysis for switched neural networks subject to stochastic disturbances and time-varying delays. First, using the multiple Lyapunov functions method, a state-dependent switching law is designed to present a stochastic passivity condition. Second, a hysteresis switching law involving both the current state and the previous value of the switching signal are presented to avoid chattering resulted from the state-dependent switching. Third, based on the average dwell-time approach, a class of switching signals is determined to guarantee the switched neural network stochastically passive. Finally, three numerical examples are provided to illustrate the characteristics of three proposed switching laws.

Pinning distributed synchronization of stochastic dynamical networks: a mixed optimization approach

This paper is concerned with the problem of pinning synchronization of nonlinear dynamical networks with multiple stochastic disturbances. Two kinds of pinning schemes are considered: 1) pinned nodes are fixed along the time evolution and 2) pinned nodes are switched from time to time according to a set of Bernoulli stochastic variables. Using Lyapunov function methods and stochastic analysis techniques, several easily verifiable criteria are derived for the problem of pinning distributed synchronization. For the case of fixed pinned nodes, a novel mixed optimization method is developed to select the pinned nodes and find feasible solutions, which is composed of a traditional convex optimization method and a constraint optimization evolutionary algorithm. For the case of switching pinning scheme, upper bounds of the convergence rate and the mean control gain are obtained theoretically. Simulation examples are provided to show the advantages of our proposed optimization method over previous ones and verify the effectiveness of the obtained results.

Robust H∞ filtering for a class of complex networks with stochastic packet dropouts and time delays

The robust H_∞ filtering problem is investigated for a class of complex network systems which has stochastic packet dropouts and time delays, combined with disturbance inputs. The packet dropout phenomenon occurs in a random way and the occurrence probability for each measurement output node is governed by an individual random variable. Besides, the time delay phenomenon is assumed to occur in a nonlinear vector-valued function. We aim to design a filter such that the estimation error converges to zero exponentially in the mean square, while the disturbance rejection attenuation is constrained to a given level by means of the H_∞ performance index. By constructing the proper Lyapunov-Krasovskii functional, we acquire sufficient conditions to guarantee the stability of the state detection observer for the discrete systems, and the observer gain is also derived by solving linear matrix inequalities. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method.

Stability and synchronization of discrete-time neural networks with switching parameters and time-varying delays

This paper is concerned with the problems of exponential stability analysis and synchronization of discrete-time switched delayed neural networks. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with time-delays. Benefitting from the delay partitioning method and the free-weighting matrix technique, the conservatism of the obtained results is reduced. In addition, the decay estimates are explicitly given and the synchronization problem is solved. The results reported in this paper not only depend upon the delay, but also depend upon the partitioning, which aims at reducing the conservatism. Numerical examples are presented to demonstrate the usefulness of the derived theoretical results.

Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data

In this paper, the problem of sampled-data synchronization for Markovian jump neural networks with time-varying delay and variable samplings is considered. In the framework of the input delay approach and the linear matrix inequality technique, two delay-dependent criteria are derived to ensure the stochastic stability of the error systems, and thus, the master systems stochastically synchronize with the slave systems. The desired mode-independent controller is designed, which depends upon the maximum sampling interval. The effectiveness and potential of the obtained results is verified by two simulation examples.