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Wang P, He Q, Su H. Stabilization of Discrete-Time Stochastic Delayed Neural Networks by Intermittent Control. IEEE TRANSACTIONS ON CYBERNETICS 2023; 53:2017-2027. [PMID: 34546937 DOI: 10.1109/tcyb.2021.3108574] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
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.
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2
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Li Y, Wang X, Li B. Stepanov-Like Almost Periodic Dynamics of Clifford-Valued Stochastic Fuzzy Neural Networks with Time-Varying Delays. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10820-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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Qu Y, Pang K. State estimation for a class of artificial neural networks subject to mixed attacks: A set-membership method. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.06.020] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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5
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An Extended Analysis on Robust Dissipativity of Uncertain Stochastic Generalized Neural Networks with Markovian Jumping Parameters. Symmetry (Basel) 2020. [DOI: 10.3390/sym12061035] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The main focus of this research is on a comprehensive analysis of robust dissipativity issues pertaining to a class of uncertain stochastic generalized neural network (USGNN) models in the presence of time-varying delays and Markovian jumping parameters (MJPs). In real-world environments, most practical systems are subject to uncertainties. As a result, we take the norm-bounded parameter uncertainties, as well as stochastic disturbances into consideration in our study. To address the task, we formulate the appropriate Lyapunov–Krasovskii functional (LKF), and through the use of effective integral inequalities, simplified linear matrix inequality (LMI) based sufficient conditions are derived. We validate the feasible solutions through numerical examples using MATLAB software. The simulation results are analyzed and discussed, which positively indicate the feasibility and effectiveness of the obtained theoretical findings.
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Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties. MATHEMATICS 2020. [DOI: 10.3390/math8050742] [Citation(s) in RCA: 42] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In practical applications, stochastic effects are normally viewed as the major sources that lead to the system’s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov–Krasovskii functional and applying Jensen’s inequality, a number of sufficient conditions can be derived by utilizing It o ^ ’s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.
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A Delay-Dividing Approach to Robust Stability of Uncertain Stochastic Complex-Valued Hopfield Delayed Neural Networks. Symmetry (Basel) 2020. [DOI: 10.3390/sym12050683] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In scientific disciplines and other engineering applications, most of the systems refer to uncertainties, because when modeling physical systems the uncertain parameters are unavoidable. In view of this, it is important to investigate dynamical systems with uncertain parameters. In the present study, a delay-dividing approach is devised to study the robust stability issue of uncertain neural networks. Specifically, the uncertain stochastic complex-valued Hopfield neural network (USCVHNN) with time delay is investigated. Here, the uncertainties of the system parameters are norm-bounded. Based on the Lyapunov mathematical approach and homeomorphism principle, the sufficient conditions for the global asymptotic stability of USCVHNN are derived. To perform this derivation, we divide a complex-valued neural network (CVNN) into two parts, namely real and imaginary, using the delay-dividing approach. All the criteria are expressed by exploiting the linear matrix inequalities (LMIs). Based on two examples, we obtain good theoretical results that ascertain the usefulness of the proposed delay-dividing approach for the USCVHNN model.
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Stability and Dissipativity Analysis for Neutral Type Stochastic Markovian Jump Static Neural Networks with Time Delays. JOURNAL OF ARTIFICIAL INTELLIGENCE AND SOFT COMPUTING RESEARCH 2019. [DOI: 10.2478/jaiscr-2019-0003] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Abstract
This paper studies the global asymptotic stability and dissipativity problem for a class of neutral type stochastic Markovian Jump Static Neural Networks (NTSMJSNNs) with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii Functional (LKF) with some augmented delay-dependent terms and by using integral inequalities to bound the derivative of the integral terms, some new sufficient conditions have been obtained, which ensure that the global asymptotic stability in the mean square. The results obtained in this paper are expressed in terms of Strict Linear Matrix Inequalities (LMIs), whose feasible solutions can be verified by effective MATLAB LMI control toolbox. Finally, examples and simulations are given to show the validity and advantages of the proposed results.
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Chen W, Huang Y, Ren S. Passivity of coupled memristive delayed neural networks with fixed and adaptive coupling weights. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.06.019] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Li XM, Chen Y, Li JY. Finite-time state estimation for delayed periodic neural networks over multiple-packet transmission. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2018.05.059] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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Xu Y, Liu C, Lu R, Su CY. Remote Estimator Design for Time-Delay Neural Networks Using Communication State Information. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:5149-5158. [PMID: 29994373 DOI: 10.1109/tnnls.2018.2793185] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This paper investigates the estimator design for the neural networks, where distributed delays and imperfect measurements are included. A randomly occurred neuron-dependent nonlinearity is used to describe the uncertain measurements disturbed by neurons. The measurements are transmitted over multiple transmission channels, and Markov chains are introduced to model packet dropouts of these channels. A one-to-one map is constructed to transform $m$ independent Markov chains to an augmented one to facilitate system analysis. A new variable called channel state is defined based on the cases of packet dropouts, and the channel-state-dependent estimator is designed to trade off between the number and the performance of the estimator. Sufficient conditions are established to guarantee that the augmented system is stochastically stable and satisfies the strict $(Q, S, R)-\gamma -$ dissipativity. The estimator gains are derived using linear matrix methods. Finally, an example is applied to illustrate the effectiveness of the developed methods.
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Liu L, Cao J, Qian C. th Moment Exponential Input-to-State Stability of Delayed Recurrent Neural Networks With Markovian Switching via Vector Lyapunov Function. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:3152-3163. [PMID: 28692993 DOI: 10.1109/tnnls.2017.2713824] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
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.
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Chen Y, Liu L, Qian W, Liu Y, Alsaadi FE. l2−l∞ state estimation for discrete-time switched neural networks with time-varying delay. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.12.006] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Wang Z, Liu X, Liu K, Li S, Wang H. Backstepping-Based Lyapunov Function Construction Using Approximate Dynamic Programming and Sum of Square Techniques. IEEE TRANSACTIONS ON CYBERNETICS 2017; 47:3393-3403. [PMID: 27337732 DOI: 10.1109/tcyb.2016.2574747] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this paper, backstepping for a class of block strict-feedback nonlinear systems is considered. Since the input function could be zero for each backstepping step, the backstepping technique cannot be applied directly. Based on the assumption that nonlinear systems are polynomials, for each backstepping step, Lypunov function can be constructed in a polynomial form by sum of square (SOS) technique. The virtual control can be obtained by the Sontag feedback formula, which is equivalent to an optimal control-the solution of a Hamilton-Jacobi-Bellman equation. Thus, approximate dynamic programming (ADP) could be used to estimate value functions (Lyapunov functions) instead of SOS. Through backstepping technique, the control Lyapunov function (CLF) of the full system is constructed finally making use of the strict-feedback structure and a stabilizable controller can be obtained through the constructed CLF. The contributions of the proposed method are twofold. On one hand, introducing ADP into backstepping can broaden the application of the backstepping technique. A class of block strict-feedback systems can be dealt by the proposed method and the requirement of nonzero input function for each backstepping step can be relaxed. On the other hand, backstepping with surface dynamic control actually reduces the computation complexity of ADP through constructing one part of the CLF by solving semidefinite programming using SOS. Simulation results verify contributions of the proposed method.
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Shan Q, Zhang H, Wang Z, Wang J. Adjustable delay interval method based stochastic robust stability analysis of delayed neural networks. Neurocomputing 2017. [DOI: 10.1016/j.neucom.2016.09.040] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Wang L, Shen Y, Zhang G. Synchronization of a Class of Switched Neural Networks with Time-Varying Delays via Nonlinear Feedback Control. IEEE TRANSACTIONS ON CYBERNETICS 2016; 46:2300-2310. [PMID: 26390507 DOI: 10.1109/tcyb.2015.2475277] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
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.
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Nonfragile l 2 - l ∞ state estimation for discrete-time neural networks with jumping saturations. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.04.002] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Nie X, Zheng WX. Dynamical Behaviors of Multiple Equilibria in Competitive Neural Networks With Discontinuous Nonmonotonic Piecewise Linear Activation Functions. IEEE TRANSACTIONS ON CYBERNETICS 2016; 46:679-693. [PMID: 25826814 DOI: 10.1109/tcyb.2015.2413212] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
This paper addresses the problem of coexistence and dynamical behaviors of multiple equilibria for competitive neural networks. First, a general class of discontinuous nonmonotonic piecewise linear activation functions is introduced for competitive neural networks. Then based on the fixed point theorem and theory of strict diagonal dominance matrix, it is shown that under some conditions, such n -neuron competitive neural networks can have 5(n) equilibria, among which 3(n) equilibria are locally stable and the others are unstable. More importantly, it is revealed that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibria and locally stable equilibria than the ones with other activation functions, such as the continuous Mexican-hat-type activation function and discontinuous two-level activation function. Furthermore, the 3(n) locally stable equilibria given in this paper are located in not only saturated regions, but also unsaturated regions, which is different from the existing results on multistability of neural networks with multiple level activation functions. A simulation example is provided to illustrate and validate the theoretical findings.
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Robust adaptive decentralized control for a class of noaffine stochastic nonlinear interconnected systems. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.06.075] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Wang Z, Liu L, Shan QH, Zhang H. Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2015; 26:2589-2595. [PMID: 25608313 DOI: 10.1109/tnnls.2014.2387434] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
A secondary delay partitioning method is proposed to study the stability problem for a class of recurrent neural networks (RNNs) with time-varying delay. The total interval of the time-varying delay is first divided into two parts, and then each part is further divided into several subintervals. To deal with the state variables associated with these subintervals, an extended reciprocal convex combination approach and a double integral term with variable upper and lower limits of integral as a Lyapunov functional are proposed, which help to obtain the stability criterion. The main feature of the proposed result is more effective for the RNNs with fast time-varying delay. A numerical example is used to show the effectiveness of the proposed stability result.
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Wang H, Liu K, Liu X, Chen B, Lin C. Neural-Based Adaptive Output-Feedback Control for a Class of Nonstrict-Feedback Stochastic Nonlinear Systems. IEEE TRANSACTIONS ON CYBERNETICS 2015; 45:1977-1987. [PMID: 25361516 DOI: 10.1109/tcyb.2014.2363073] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
In this paper, we consider the problem of observer-based adaptive neural output-feedback control for a class of stochastic nonlinear systems with nonstrict-feedback structure. To overcome the design difficulty from the nonstrict-feedback structure, a variable separation approach is introduced by using the monotonically increasing property of system bounding functions. On the basis of the state observer, and by combining the adaptive backstepping technique with radial basis function neural networks' universal approximation capability, an adaptive neural output feedback control algorithm is presented. It is shown that the proposed controller can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in the sense of mean quartic value. Simulation results are provided to show the effectiveness of the proposed control scheme.
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Finite-time robust passive control for a class of uncertain Lipschitz nonlinear systems with time-delays. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.01.038] [Citation(s) in RCA: 68] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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23
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Reliable stabilization for memristor-based recurrent neural networks with time-varying delays. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.11.043] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Su L, Shen H. Fault-tolerant dissipative synchronization for chaotic systems based on fuzzy mixed delayed feedback. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.10.049] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Tan H, Hua M, Chen J, Fei J. Stability analysis of stochastic Markovian switching static neural networks with asynchronous mode-dependent delays. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2014.10.009] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Stability and Bifurcation of a Class of Discrete-Time Cohen–Grossberg Neural Networks with Discrete Delays. Neural Process Lett 2013. [DOI: 10.1007/s11063-013-9329-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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