Distributed Nash equilibrium seeking in noncooperative game with partial decision information of neighbors

In the real world, individuals may conceal some of their real decision information to their neighbors due to competition. It is a challenge to explore the distributed Nash equilibrium when individuals play the noncooperative game with partial decision information in complex networks. In this paper, we investigate the distributed Nash equilibrium seeking problem with partial decision information of neighbors. Specifically, we construct a two-layer network model, where players in the first layer engage in game interactions and players in the second layer exchange estimations of real actions with each other. We also consider the case where the actions of some players remain unchanged due to the cost of updating or personal reluctance. By means of the Lyapunov function method and LaSalle's invariance principle, we obtain the sufficient conditions in which the consensus of individual actions and estimations can be achieved and the population actions can converge to the Nash equilibrium point. Furthermore, we investigate the case with switched topologies and derive the sufficient conditions for the convergence of individual actions to Nash equilibrium by the average dwell time method. Finally, we give numerical examples for cases of fixed and switched topologies to verify our theoretical results.

Stability and synchronization for complex-valued neural networks with stochastic parameters and mixed time delays

In this paper, a class of complex-valued neural networks (CVNNs) with stochastic parameters and mixed time delays are proposed. The random fluctuation of system parameters is considered in order to describe the implementation of CVNNs more practically. Mixed time delays including distributed delays and time-varying delays are also taken into account in order to reflect the influence of network loads and communication constraints. Firstly, the stability problem is investigated for the CVNNs. In virtue of Lyapunov stability theory, a sufficient condition is deduced to ensure that CVNNs are asymptotically stable in the mean square. Then, for an array of coupled identical CVNNs with stochastic parameters and mixed time delays, synchronization issue is investigated. A set of matrix inequalities are obtained by using Lyapunov stability theory and Kronecker product and if these matrix inequalities are feasible, the addressed CVNNs are synchronized. Finally, the effectiveness of the obtained theoretical results is demonstrated by two numerical examples.

Stabilization of Discrete-Time Stochastic Delayed Neural Networks by Intermittent Control

This article investigates the stabilization of discrete-time stochastic neural networks with time-varying delay via aperiodically intermittent control (AIC). A comprehensive analysis of the stabilization of discrete-time delayed systems via AIC is provided, where the Lyapunov function method and the Lyapunov-Krasovskii functional method are investigated, respectively. Then, three stabilization criteria are given, which extend previous works from the continuous-time framework to the discrete-time one, and the average activation time ratio (AATR) of AIC is estimated. It is highlighted that for the Lyapunov-Krasovskii functional method, a more flexible estimation for the AATR can be obtained. Finally, the differences and the advantages of the three stabilization criteria are illustrated by numerical simulations.

Finite-Time Estimation for Markovian BAM Neural Networks With Asymmetrical Mode-Dependent Delays and Inconstant Measurements

The issue of finite-time state estimation is studied for discrete-time Markovian bidirectional associative memory neural networks. The asymmetrical system mode-dependent (SMD) time-varying delays (TVDs) are considered, which means that the interval of TVDs is SMD. Because the sensors are inevitably influenced by the measurement environments and indirectly influenced by the system mode, a Markov chain, whose transition probability matrix is SMD, is used to describe the inconstant measurement. A nonfragile estimator is designed to improve the robustness of the estimator. The stochastically finite-time bounded stability is guaranteed under certain conditions. Finally, an example is used to clarify the effectiveness of the state estimation.

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.

Nonfragile H∞ Synchronization of BAM Inertial Neural Networks Subject to Persistent Dwell-Time Switching Regularity

This article concentrates on the synchronization of discrete-time persistent dwell-time (PDT) switched bidirectional associative memory inertial neural networks with time-varying delays. Through the use of the switched system theory related to the PDT, the convex optimization technique together with some straightforward decoupling methods, an appropriate mode-dependent controller with nonfragility is developed to acclimatize itself to some practical circumstances. Simultaneously, sufficient conditions of ensuring the H_∞ performance and exponential stability for the resulting switched synchronization error system are derived. Finally, a numerical example is utilized to show the validity of the model constructed and the influence of the PDT on the H_∞ performance. In addition, an image encryption example is employed to show the potential application prospect of the investigated system.

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 Filtering for Delayed Markov Jump Nonlinear Systems with Unknown Probabilities

This paper focuses on the problem of event-triggered H∞ asynchronous filtering for Markov jump nonlinear systems with varying delay and unknown probabilities. An event-triggered scheduling scheme is adopted to decrease the transmission rate of measured outputs. The devised filter is mode dependent and asynchronous with the original system, which is represented by a hidden Markov model (HMM). Both the probability information involved in the original system and the filter are assumed to be only partly available. Under this framework, via employing the Lyapunov–Krasovskii functional and matrix inequality transformation techniques, a sufficient condition is given and the filter is further devised to ensure that the resulting filtering error dynamic system is stochastically stable with a desired H∞ disturbance attenuation performance. Lastly, the validity of the presented filter design scheme is verified through a numerical example.

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.

Synchronization of Switched Discrete-Time Neural Networks via Quantized Output Control With Actuator Fault

This article considers global exponential synchronization almost surely (GES a.s.) for a class of switched discrete-time neural networks (DTNNs). The considered system switches from one mode to another according to transition probability (TP) and evolves with mode-dependent average dwell time (MDADT), i.e., TP-based MDADT switching, which is more practical than classical average dwell time (ADT) switching. The logarithmic quantization technique is utilized to design mode-dependent quantized output controllers (QOCs). Noticing that external perturbations are unavoidable, actuator fault (AF) is also considered. New Lyapunov-Krasovskii functionals and analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. It is discovered that the TP matrix plays an important role in achieving the GES a.s., the upper bound of the dwell time (DT) of unsynchronized subsystems can be very large, and the lower bound of the DT of synchronized subsystems can be very small. An algorithm is given to design the control gains, and an optimal algorithm is provided for reducing conservatism of the given results. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

Anti-Synchronization of Delayed State-Based Switched Inertial Neural Networks

In this article, global anti-synchronization control for a class of state-based switched inertial neural networks (SBSINNs) with time-varying delays is considered. Based on the hybrid control strategies and Lyapunov stability theory, several criteria are obtained to ensure global anti-synchronization of the underlying SBSINNs. Furthermore, we consider the global asymptotic anti-synchronization directly from the SBSINNs themselves with a nonreduced-order method. Finally, a numerical simulation is given to illustrate the effectiveness of the results.

Event-Based Dissipative Filtering of Markovian Jump Neural Networks Subject to Incomplete Measurements and Stochastic Cyber-Attacks

In this article, the dissipativity-based filtering of the Markovian jump neural networks subject to incomplete measurements and deception attacks is investigated by adopting an event-triggered communication strategy, where the attackers are supposed to occur in a random fashion but obey the Bernoulli distribution. Consider that the information of the system mode is transmitted to the filter over the communication network that is vulnerable to external attacks, which may lead to the undesired performance of the resulting system by injecting malicious information from the attackers. As a result, the filter has difficulty completing information from the original system. Besides, an event-triggered communication mechanism is introduced to reduce the communication frequency between data transmission due to the limited network resources, and different triggering conditions corresponding to different jump modes are developed. Then, based on the above considerations, the sufficient condition is derived to ensure the stochastic stability and dissipativity of the resulting augmented system although the deception attacks and incomplete information exist. A numerical simulated example is provided to verify the theoretical analysis.

Global exponential stabilization and lag synchronization control of inertial neural networks with time delays

The global exponential stabilization and lag synchronization control of delayed inertial neural networks (INNs) are investigated. By constructing nonnegative function and employing inequality techniques, several new results about exponential stabilization and exponential lag synchronization are derived via adaptive control. And the theoretical outcomes are developed directly from the INNs themselves without variable substitution. In addition, the synchronization results are also applied to image encryption and decryption. Finally, an example is presented to illustrate the validity of the derived 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.

Exponential Synchronization and L2 -Gain Analysis of Delayed Chaotic Neural Networks Via Intermittent Control With Actuator Saturation

By using an intermittent control approach, this paper is concerned with the exponential synchronization and L₂ -gain analysis for a class of delayed master-slave chaotic neural networks subject to actuator saturation. Based on a switching strategy, the synchronization error system is modeled as a switched synchronization error system consisting of two subsystems, and each subsystem of the switched system satisfies a dwell time constraint due to the characteristics of intermittent control. A piecewise Lyapunov-Krasovskii functional depending on the control rate and control period is then introduced, under which sufficient conditions for the exponential stability of the constructed switched synchronization error system are developed. In addition, the influence of the exogenous perturbations on synchronization performance is constrained at a prescribed level. In the meantime, the intermittent linear state feedback controller can be derived by solving a set of linear matrix inequalities. More incisively, the proposed method is also proved to be valid in the case of aperiodically intermittent control. Finally, two simulation examples are employed to demonstrate the effectiveness and potential of the obtained results.

Finite-Time Synchronization of Markovian Jumping Complex Networks with Non-Identical Nodes and Impulsive Effects

In this paper, we investigate the finite-time synchronization problem for a class of Markovian jumping complex networks (MJCNs) with non-identical nodes and impulsive effects. Sufficient conditions for the MJCNs are presented based on an M-matrix technique, Lyapunov function method, stochastic analysis technique, and suitable comparison systems to guarantee finite-time synchronization. At last, numerical examples are exploited to illustrate our theoretical results, and they testify the effectiveness of our results for complex dynamic systems.

Asynchronous and Resilient Filtering for Markovian Jump Neural Networks Subject to Extended Dissipativity

The problem of asynchronous and resilient filtering for discrete-time Markov jump neural networks subject to extended dissipativity is investigated in this paper. The modes of the designed resilient filter are assumed to run asynchronously with the modes of original Markov jump neural networks, which accord well with practical applications and are described through a hidden Markov model. Due to the fluctuation of the filter parameters, a resilient filter taking into account parameter uncertainty is adopted. Being different from the norm-bound type of uncertainty which has been studied in a considerable number of the existing literatures, the interval type of uncertainty is introduced so as to describe uncertain phenomenon more accurately. By means of convex optimal method, the gains of filter are derived to guarantee the stochastic stability and extended dissipativity of the filtering error system under the wave of the filter parameters. Considering the limited computing power of MATLAB solver, a relatively simple simulation is exploited to verify the effectiveness and merits of the theoretical findings where the relationships among optimal performance index, uncertain parameter σ , and asynchronous rate are revealed.

Generalized State Estimation for Markovian Coupled Networks Under Round-Robin Protocol and Redundant Channels

In this paper, the problem of generalized state estimation for an array of Markovian coupled networks under the round-Robin protocol (RRP) and redundant channels is investigated by using an extended dissipative property. The randomly varying coupling of the networks under consideration is governed by a Markov chain. With the aid of using the RRP, the transmission order of nodes is availably orchestrated. In this case, the probability of occurrence data collisions through a shared constrained network may be reduced. The redundant channels are also used in the signal transmission to deal with the frangibility of networks caused by a single channel in the networks. The network induced phenomena, that is, randomly occurring packet dropouts and randomly occurring quantization are fully considered. The main purpose of the research is to find a desired estimator design approach such that the extended (Ω₁,Ω₂,Ω₃) - γ -stochastic dissipativity property of the estimation error system is guaranteed. In terms of the Lyapunov-Krasovskii methodology, the Kronecker product and an improved matrix decoupling approach, sufficient conditions for such an addressed problem are established by means of handling some convex optimization problems. Finally, the serviceability of the proposed method is explained by providing an illustrated example.

Reduced-Order Filtering of Delayed Static Neural Networks With Markovian Jumping Parameters

The reduced-order filtering problems are investigated in this paper for static neural networks with Markovian jumping parameters and mode-dependent time-varying delays. By fully making use of integral inequalities, the designs of reduced-order and filters are discussed. The proper gain matrices of filters and the optimal performance indices are efficiently obtained by resolving corresponding convex optimization problems with the constraints of linear matrix inequalities. It is verified that the computational complexity for the reduced-order filter design is significantly reduced when compared with the full-order one. Furthermore, the nonfragile reduced-order filtering problems are also resolved in this paper. Two examples with simulation results are presented to demonstrate the feasibility and application of the established results.

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.

Dissipativity-Based Resilient Filtering of Periodic Markovian Jump Neural Networks With Quantized Measurements

The problem of dissipativity-based resilient filtering for discrete-time periodic Markov jump neural networks in the presence of quantized measurements is investigated in this paper. Due to the limited capacities of network medium, a logarithmic quantizer is applied to the underlying systems. Considering the fact that the filter is realized through a network, randomly occurring parameter uncertainties of the filter are modeled by two mode-dependent Bernoulli processes. By establishing the mode-dependent periodic Lyapunov function, sufficient conditions are given to ensure the stability and dissipativity of the filtering error system. The filter parameters are derived via solving a set of linear matrix inequalities. The merits and validity of the proposed design techniques are verified by a simulation example.

Synchronization of General Chaotic Neural Networks With Nonuniform Sampling and Packet Missing: A Switched System Approach

This paper is concerned with the exponential synchronization issue of general chaotic neural networks subject to nonuniform sampling and control packet missing in the frame of the zero-input strategy. Based on this strategy, we make use of the switched system model to describe the synchronization error system. First, when the missing of control packet does not occur, an exponential stability criterion with less conservatism is established for the resultant synchronization error systems via a superior time-dependent Lyapunov functional and the convex optimization approach. The characteristics induced by nonuniform sampling can be used to the full because of the structure and property of the constructed Lyapunov functional, that is not necessary to be positive definite except sampling times. Then, a criterion is obtained to guarantee that the general chaotic neural networks are synchronous exponentially when the missing of control packet occurs by means of the average dwell-time technique. An explicit expression of the sampled-data static output feedback controller is also gained. Finally, the effectiveness of the proposed new design methods is shown via two examples.

Finite-Time Stability Analysis for Markovian Jump Memristive Neural Networks With Partly Unknown Transition Probabilities

This paper is concerned with the finite-time stochastically stability (FTSS) analysis of Markovian jump memristive neural networks with partly unknown transition probabilities. In the neural networks, there exist a group of modes determined by Markov chain, and thus, the Markovian jump was taken into consideration and the concept of FTSS is first introduced for the memristive model. By introducing a Markov switching Lyapunov functional and stochastic analysis theory, an FTSS test procedure is proposed, from which we can conclude that the settling time function is a stochastic variable and its expectation is finite. The system under consideration is quite general since it contains completely known and completely unknown transition probabilities as two special cases. More importantly, a nonlinear measure method was introduced to verify the uniqueness of the equilibrium point; compared with the fixed point Theorem that has been widely used in the existing results, this method is more easy to implement. Besides, the delay interval was divided into four subintervals, which make full use of the information of the subsystems upper bounds of the time-varying delays. Finally, the effectiveness and superiority of the proposed method is demonstrated by two simulation examples.