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

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.

Robust Composite H∞ Synchronization of Markov Jump Reaction-Diffusion Neural Networks via a Disturbance Observer-Based Method

This article focuses on the composite H_∞ synchronization problem for jumping reaction-diffusion neural networks (NNs) with multiple kinds of disturbances. Due to the existence of disturbance effects, the performance of the aforementioned system would be degraded; therefore, improving the control performance of closed-loop NNs is the main goal of this article. Notably, for these disturbances, one of them can be described as a norm-bounded, and the other is generated by an exogenous model. In order to reject the above one kind of disturbance, a disturbance observer is developed. Furthermore, combining the disturbance observer approach and conventional state-feedback control scheme, a composite disturbance rejection controller is specifically designed to compensate for the influences of the disturbances. Then, some criteria are established based on the general Lyapunov stability theory, which can ensure that the synchronization error system is stochastically stable and satisfies a fixed H_∞ performance level. A simulation example is finally presented to verify the availability of our developed method.

Dissipativity-based synthesis for semi-Markovian systems with simultaneous probabilistic sensors and actuators faults: A modified event-triggered strategy

Aided by a modified event-triggered communication policy (ETCP), this article addresses the dissipativity-based control synthesis problem for semi-Markovian switching systems (SMSSs) with simultaneous multiplicative probabilistic faults on sensors and actuators modules. The resulting model under consideration is more extensive, which covers semi-Markovian switching coefficients, transmission delays, and randomly occurring sensors and actuators faults in a unified systematic analytical framework instead of investigating separately in some existing works. More specifically, the probabilistic faults are assumed to happen on both the sensors and actuators modules simultaneously, and the distortion probability for each sensor and actuator is irrelevant, which can be characterized by multiplicate mutually independent stochastic variables that obeys certain statistical features and probabilistic distribution delineate on the interval [0,✠](✠≥1). To reduce the bandwidth usage, a novel event-triggered strategy is designed. Additionally, in the light of this newly developed ETCP, and considering the effects of the signal transmission delays and multitudinous probabilistic failures, a generalized and more realistic faulty pattern for SMSSs is presented, which is more fit for real applications. Hereby, the principal superiority of the established new type faulty pattern lies in its practicality and generality, which contains some previous faulty models as special scenarios. By constructing an appropriate semi-Markovian Lyapunov functional (SMLF) together with mathematical analysis technique and matrix inequality decoupling operation, sojourn-time-dependent sufficient conditions for determining both the control gain matrices and triggered configuration coefficients are developed and formulated in terms of a group of feasible linear matrix inequalities (LMIs). Eventually, several practical examples are exploited to substantiate the validity and practicability of the developed control design methodology.

H∞ State Estimation for BAM Neural Networks With Binary Mode Switching and Distributed Leakage Delays Under Periodic Scheduling Protocol

This article is concerned with the H_∞ state estimation problem for a class of bidirectional associative memory (BAM) neural networks with binary mode switching, where the distributed delays are included in the leakage terms. A couple of stochastic variables taking values of 1 or 0 are introduced to characterize the switching behavior between the redundant models of the BAM neural network, and a general type of neuron activation function (i.e., the sector-bounded nonlinearity) is considered. In order to prevent the data transmissions from collisions, a periodic scheduling protocol (i.e., round-robin protocol) is adopted to orchestrate the transmission order of sensors. The purpose of this work is to develop a full-order estimator such that the error dynamics of the state estimation is exponentially mean-square stable and the H_∞ performance requirement of the output estimation error is also achieved. Sufficient conditions are established to ensure the existence of the required estimator by constructing a mode-dependent Lyapunov-Krasovskii functional. Then, the desired estimator parameters are obtained by solving a set of matrix inequalities. Finally, a numerical example is provided to show the effectiveness of the proposed estimator design method.

Distributed tracking control of structural balance for complex dynamical networks based on the coupling targets of nodes and links

In this paper, the complex dynamical networks (CDNs) with dynamic connections are regarded as an interconnected systems composed of intercoupling links’ subsystem (LS) and nodes’ subsystem (NS). Different from the previous researches on structural balance control of CDNs, the directed CDNs’ structural balance problem is solved. Considering the state of links cannot be measured accurately in practice, we can control the nodes’ state and enforce the weights of links to satisfy the conditions of structural balance via effective coupling. To achieve this aim, a coupling strategy between a predetermined matrix of the structural balance and a reference tracking target of NS is established by the correlative control method. Here, the controller in NS is used to track the reference tracking target, and indirectly let LS track the predetermined matrix and reach a structural balance by the effective coupling for directed and undirected networks. Finally, numerical simulations are presented to verify the theoretical results.

Distributed Nesterov Gradient and Heavy-Ball Double Accelerated Asynchronous Optimization

In this article, we come up with a novel Nesterov gradient and heavy-ball double accelerated distributed synchronous optimization algorithm, called NHDA, and adopt a general asynchronous model to further propose an effective asynchronous algorithm, called ASY-NHDA, for distributed optimization problem over directed graphs, where each agent has access to a local objective function and computes the optimal solution via communicating only with its immediate neighbors. Our goal is to minimize a sum of all local objective functions satisfying strong convexity and Lipschitz continuity. Consider a general asynchronous model, where agents communicate with their immediate neighbors and start a new computation independently, that is, agents can communicate with their neighbors at any time without any coordination and use delayed information from their in-neighbors to compute a new update. Delays are arbitrary, unpredictable, and time-varying but bounded. The theoretical analysis of NHDA is based on analyzing the interaction among the consensus, the gradient tracking, and the optimization processes. As for the analysis of ASY-NHDA, we equivalently transform the asynchronous system into an augmented synchronous system without delays and prove its convergence through using the generalized small gain theorem. The results show that NHDA and ASY-NHDA converge to the optimal solution at a linear convergence as long as the largest step size is positive and less than an explicitly estimated upper bound, and the largest momentum parameter is nonnegative and less than an upper bound. Finally, we demonstrate the advantages of ASY-NHDA through simulations.

Finite- and Fixed-Time Cluster Synchronization of Nonlinearly Coupled Delayed Neural Networks via Pinning Control

In this article, the cluster synchronization problem for a class of the nonlinearly coupled delayed neural networks (NNs) in both finite- and fixed-time cases are investigated. Based on the Lyapunov stability theory and pinning control strategy, some criteria are provided to ensure the cluster synchronization of the nonlinearly coupled delayed NNs in both finite-and fixed-time aspects. Then, the settling time for stabilization that is dependent on the initial value and independent of the initial value is estimated, respectively. Finally, we illustrate the feasibility and practicality of the results via a numerical example.

Memory-Event-Triggered H∞ Output Control of Neural Networks With Mixed Delays

This article investigates the problem of memory-event-triggered H∞ output feedback control for neural networks with mixed delays (discrete and distributed delays). The probability density of the communication delay among neurons is modeled as the kernel of the distributed delay. To reduce network communication burden, a novel memory-event-triggered scheme (METS) using the historical system output is introduced to choose which data should be sent to the controller. Based on a constructed Lyapunov-Krasovskii functional (LKF) with the distributed delay kernel and a generalized integral inequality, new sufficient conditions are formed by linear matrix inequalities (LMIs) for designing an event-triggered H∞ controller. Finally, experiments based on a computer and a real wireless network are executed to confirm the validity of the developed method.

H∞ estimation for stochastic semi-Markovian switching CVNNs with missing measurements and mode-dependent delays

This article is devoted to the H_∞ estimation problem for stochastic semi-Markovian switching complex-valued neural networks subject to incomplete measurement outputs, where the time-varying delay also depends on another semi-Markov process. A sequence of random variables with known statistical property is introduced to depict the missing measurement phenomenon. Based on the generalized Itoˆ's formula in complex form concerning with the semi-Markovian systems, complex-valued reciprocal convex inequality as well as intensive stochastic analysis method, some mode-dependent sufficient conditions are presented guaranteeing the estimation error system to be exponentially mean-square stable with a prespecified H_∞ disturbance attenuation level. In addition, the mode-dependent estimator gain matrices are appropriately designed according to the feasible solutions of certain complex matrix inequalities. In the end, one numerical example is provided to illustrate effectiveness of the theoretical results.

Steady-State Design of Large-Dimensional Boolean Networks

Analysis and design of steady states representing cell types, such as cell death or unregulated growth, are of significant interest in modeling genetic regulatory networks. In this article, the steady-state design of large-dimensional Boolean networks (BNs) is studied via model reduction and pinning control. Compared with existing literature, the pinning control design in this article is based on the original node's connection, but not on the state-transition matrix of BNs. Hence, the computational complexity is dramatically reduced in this article from O(2ⁿ×2ⁿ) to O(2×2^r) , where n is the number of nodes in the large-dimensional BN and is the largest number of in-neighbors of the reduced BN. Finally, the proposed method is well demonstrated by a T-LGL survival signaling network with 18 nodes and a model of survival signaling in large granular lymphocyte leukemia with 29 nodes. Just as shown in the simulations, the model reduction method reduces 99.98% redundant states for the network with 18 nodes, and 99.99% redundant states for the network with 29 nodes.

Synchronization for Quantized Semi-Markov Switching Neural Networks in a Finite Time

Finite-time synchronization (FTS) is discussed for delayed semi-Markov switching neural networks (S-MSNNs) with quantized measurement, in which a logarithmic quantizer is employed. The stochastic phenomena of structural and parametrical changes are modeled by a semi-Markov process whose transition rates are time-varying to depend on the sojourn time. Practical systems subject to unpredictable structural changes, such as quadruple-tank process systems, are described by delayed S-MSNNs. A key issue under the consideration is how to design a feedback controller to guarantee the FTS between the master system and the slave system. For this purpose, by using the weak infinitesimal operator, sufficient conditions are constructed to realize FTS of the resulting error system over a finite-time interval. Then, the solvability conditions for the desired finite-time controller can be determined under a linear matrix inequality framework. Finally, the theoretical findings are illustrated by the quadruple-tank process model.

Synchronization of Coupled Time-Delay Neural Networks With Mode-Dependent Average Dwell Time Switching

In the literature, the effects of switching with average dwell time (ADT), Markovian switching, and intermittent coupling on stability and synchronization of dynamic systems have been extensively investigated. However, all of them are considered separately because it seems that the three kinds of switching are different from each other. This article proposes a new concept to unify these switchings and considers global exponential synchronization almost surely (GES a.s.) in an array of neural networks (NNs) with mixed delays (including time-varying delay and unbounded distributed delay), switching topology, and stochastic perturbations. A general switching mechanism with transition probability (TP) and mode-dependent ADT (MDADT) (i.e., TP-based MDADT switching in this article) is introduced. By designing a multiple Lyapunov-Krasovskii functional and developing a set of new analytical techniques, sufficient conditions are obtained to ensure that the coupled NNs with the general switching topology achieve GES a.s., even in the case that there are both synchronizing and nonsynchronizing modes. Our results have removed the restrictive condition that the increment coefficients of the multiple Lyapunov-Krasovskii functional at switching instants are larger than one. As applications, the coupled NNs with Markovian switching topology and intermittent coupling are employed. Numerical examples are provided to demonstrate the effectiveness and the merits of the theoretical analysis.

Stochastic Finite-Time H∞ State Estimation for Discrete-Time Semi-Markovian Jump Neural Networks With Time-Varying Delays

In this article, the finite-time H_∞ state estimation problem is addressed for a class of discrete-time neural networks with semi-Markovian jump parameters and time-varying delays. The focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite-time bounded with a prescribed H_∞ performance level via finite-time Lyapunov stability theory. By constructing a delay-product-type Lyapunov functional, in which the information of time-varying delays and characteristics of activation functions are fully taken into account, and using the Jensen summation inequality, the free weighting matrix approach, and the extended reciprocally convex matrix inequality, some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator. Finally, numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results.

RNN for Perturbed Manipulability Optimization of Manipulators Based on a Distributed Scheme: A Game-Theoretic Perspective

In order to leverage the unique advantages of redundant manipulators, avoiding the singularity during motion planning and control should be considered as a fundamental issue to handle. In this article, a distributed scheme is proposed to improve the manipulability of redundant manipulators in a group. To this end, the manipulability index is incorporated into the cooperative control of multiple manipulators in a distributed network, which is used to guide manipulators to adjust to the optimal spatial position. Moreover, from the perspective of game theory, this article formulates the problem into a Nash equilibrium. Then, a neural network with anti-noise ability is constructed to seek and approximate the optimal strategy profile of the Nash equilibrium problem with time-varying parameters. Theoretical analyses show that the neural network model has the superior global convergence and noise immunity. Finally, simulation results demonstrate that the neural network is effective in real-time cooperative motion generation of multiple redundant manipulators under perturbations in distributed networks.

Event-Triggered Synchronization for Neutral-Type Semi-Markovian Neural Networks With Partial Mode-Dependent Time-Varying Delays

This article studies the event-triggered stochastic synchronization problem for neutral-type semi-Markovian jump (SMJ) neural networks with partial mode-dependent additive time-varying delays (ATDs), where the SMJ parameters in two ATDs are considered to be not completely the same as the one in the connection weight matrices of the systems. Different from the weak infinitesimal operator of multi-Markov processes, a new one for the double semi-Markovian processes (SMPs) is first proposed. To reduce the conservative of the stability criteria, a generalized reciprocally convex combination inequality (RCCI) is established by the virtue of an interesting technique. Then, based on an eligible stochastic Lyapunov-Krasovski functional, three novel stability criteria for the studied systems are derived by employing the new RCCI and combining with a well-designed event-triggered control scheme. Finally, three numerical examples and one practical engineering example are presented to show the validity of our methods.

A Deterministic Annealing Neural Network Algorithm for the Minimum Concave Cost Transportation Problem

In this article, a deterministic annealing neural network algorithm is proposed to solve the minimum concave cost transportation problem. Specifically, the algorithm is derived from two neural network models and Lagrange-barrier functions. The Lagrange function is used to handle linear equality constraints, and the barrier function is used to force the solution to move to the global or near-global optimal solution. In both neural network models, two descent directions are constructed, and an iterative procedure for the optimization of the neural network is proposed. As a result, two corresponding Lyapunov functions are naturally obtained from these two descent directions. Furthermore, the proposed neural network models are proved to be completely stable and converge to the stable equilibrium state, therefore, the proposed algorithm converges. At last, the computer simulations on several test problems are made, and the results indicate that the proposed algorithm always generates global or near-global optimal solutions.

Synchronization of Time-Delayed Complex Networks With Switching Topology Via Hybrid Actuator Fault and Impulsive Effects Control

This article investigates global exponential synchronization almost surely (GES a.s.) of complex networks (CNs) with node delay and switching topology. By introducing transition probability (TP) and mode-dependent average dwell time (MDADT) to the switching signal, the considered model is more practical than the systems with average dwell-time (ADT) switching. Controllers with both impulsive effects and actuator fault feedback are considered. New analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. Different from the existing results on the synchronization of switched systems, our results show that the GES a.s. can still be achieved even in the case that the upper bound of the dwell time (DT) of uncontrolled nodes is very large and the lower bound of the DT of controlled nodes is very small. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

Barrier Function-Based Adaptive Control for Uncertain Strict-Feedback Systems Within Predefined Neural Network Approximation Sets

In this article, a globally stable adaptive control strategy for uncertain strict-feedback systems is proposed within predefined neural network (NN) approximation sets, despite the presence of unknown system nonlinearities. In contrast to the conventional adaptive NN control results in the literature, a primary benefit of the developed approach is that the barrier Lyapunov function is employed to predefine the compact set for maintaining the validity of NN approximation at each step, thus accomplishing the global boundedness of all the closed-loop signals. Simulation results are performed to clarify the effectiveness of the proposed methodology.

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.

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.

An approximation algorithm for graph partitioning via deterministic annealing neural network

Graph partitioning, a classical NP-hard combinatorial optimization problem, is widely applied to industrial or management problems. In this study, an approximated solution of the graph partitioning problem is obtained by using a deterministic annealing neural network algorithm. The algorithm is a continuation method that attempts to obtain a high-quality solution by following a path of minimum points of a barrier problem as the barrier parameter is reduced from a sufficiently large positive number to 0. With the barrier parameter assumed to be any positive number, one minimum solution of the barrier problem can be found by the algorithm in a feasible descent direction. With a globally convergent iterative procedure, the feasible descent direction could be obtained by renewing Lagrange multipliers red. A distinctive feature of it is that the upper and lower bounds on the variables will be automatically satisfied on the condition that the step length is a value from 0 to 1. Four well-known algorithms are compared with the proposed one on 100 test samples. Simulation results show effectiveness of the proposed algorithm.

Nonfragile Dissipative Synchronization for Markovian Memristive Neural Networks: A Gain-Scheduled Control Scheme

In this paper, the dissipative synchronization control problem for Markovian jump memristive neural networks (MNNs) is addressed with fully considering the time-varying delays and the fragility problem in the process of implementing the gain-scheduled controller. A Markov jump model is introduced to describe the stochastic changing among the connection of MNNs and it makes the networks under consideration suitable for some actual circumstances. By utilizing some improved integral inequalities and constructing a proper Lyapunov-Krasovskii functional, several delay-dependent synchronization criteria with less conservatism are established to ensure the dynamic error system is strictly stochastically dissipative. Based on these criteria, the procedure of designing the desired nonfragile gain-scheduled controller is established, which can well handle the fragility problem in the process of implementing the controller. Finally, an illustrated example is employed to explain that the developed method is efficient and available.

Finite-Time Passivity-Based Stability Criteria for Delayed Discrete-Time Neural Networks via New Weighted Summation Inequalities

In this paper, we study the problem of finite-time stability and passivity criteria for discrete-time neural networks (DNNs) with variable delays. The main objective is how to effectively evaluate the finite-time passivity conditions for NNs. To achieve this, some new weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of a novel Lyapunov-Krasovskii functional, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed results.

Neighborhood preserving neural network for fault detection

A novel statistical feature extraction method, called the neighborhood preserving neural network (NPNN), is proposed in this paper. NPNN can be viewed as a nonlinear data-driven fault detection technique through preserving the local geometrical structure of normal process data. The "local geometrical structure " means that each sample can be constructed as a linear combination of its neighbors. NPNN is characterized by adaptively training a nonlinear neural network which takes the local geometrical structure of the data into consideration. Moreover, in order to extract uncorrelated and faithful features, NPNN adopts orthogonal constraints in the objective function. Through backpropagation and eigen decomposition (ED) technique, NPNN is optimized to extract low-dimensional features from original high-dimensional process data. After nonlinear feature extraction, Hotelling T² statistic and the squared prediction error (SPE) statistic are utilized for the fault detection tasks. The advantages of the proposed NPNN method are demonstrated by both theoretical analysis and case studies on the Tennessee Eastman (TE) benchmark process. Extensive experimental results show the superiority of NPNN in terms of missed detection rate (MDR) and false alarm rate (FAR). The source code of NPNN can be found in https://github.com/htzhaoecust/npnn.

Non-linear ICA Analysis of Resting-State fMRI in Mild Cognitive Impairment

Compared to linear independent component analysis (ICA), non-linear ICA is more suitable for the decomposition of mixed components. Existing studies of functional magnetic resonance imaging (fMRI) data by using linear ICA assume that the brain's mixed signals, which are caused by the activity of brain, are formed through the linear combination of source signals. But the application of the non-linear combination of source signals is more suitable for the mixed signals of brain. For this reason, we investigated statistical differences in resting state networks (RSNs) on 32 healthy controls (HC) and 38 mild cognitive impairment (MCI) patients using post-nonlinear ICA. Post-nonlinear ICA is one of the non-linear ICA methods. Firstly, the fMRI data of all subjects was preprocessed. The second step was to extract independent components (ICs) of fMRI data of all subjects. In the third step, we calculated the correlation coefficient between ICs and RSN templates, and selected ICs of the largest spatial correlation coefficient. The ICs represent the corresponding RSNs. After finding out the eight RSNs of MCI group and HC group, one sample t-tests were performed. Finally, in order to compare the differences of RSNs between MCI and HC groups, the two-sample t-tests were carried out. We found that the functional connectivity (FC) of RSNs in MCI patients was abnormal. Compared with HC, MCI patients showed the increased and decreased FC in default mode network (DMN), central executive network (CEN), dorsal attention network (DAN), somato-motor network (SMN), visual network(VN), MCI patients displayed the specifically decreased FC in auditory network (AN), self-referential network (SRN). The FC of core network (CN) did not reveal significant group difference. The results indicate that the abnormal FC in RSNs is selective in MCI patients.

Stabilization of Discrete-Time Markovian Jump Systems by a Partially Mode-Unmatched Fault-Tolerant Controller

In this paper, a kind of fault-tolerant controller is proposed to study the stabilization problem of discrete-time Markovian jump systems, whose operation modes are not only partially-available but also unmatched. Here, such general properties of controller are modeled to be a controller having polytopic forms and uncertainties simultaneously. Based on the proposed model, concise conditions for the existence of such a controller are proposed with linear matrix inequality (LMI) forms, which are extended to consider observer design problem too. Compared with the traditional methods, not only is the designed controller more general but also the established results are fault free and could be solved directly. Finally, numerical examples are used to demonstrate the effectiveness of the proposed methods.