1
|
Li HL, Cao J, Hu C, Zhang L, Jiang H. Adaptive control-based synchronization of discrete-time fractional-order fuzzy neural networks with time-varying delays. Neural Netw 2023; 168:59-73. [PMID: 37742532 DOI: 10.1016/j.neunet.2023.09.019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2023] [Revised: 08/11/2023] [Accepted: 09/10/2023] [Indexed: 09/26/2023]
Abstract
This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ-difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a novel discrete-time adaptive controller with time-varying delay is designed, by virtue of 1-norm Lyapunov function and newly established lemmas herein as well as inequality techniques and contradiction method, some judgement conditions are derived to guarantee complete synchronization for the explored DFFNNs. Benefitting from discrete-time adaptive control strategy and our analysis method, the conservatism of the derived synchronization criteria is reduced. Ultimately, the effectiveness of our theoretical results and secure communication scheme are demonstrated through two numerical examples.
Collapse
Affiliation(s)
- Hong-Li Li
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; School of Mathematics, Southeast University, Nanjing 210096, China.
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China; Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea.
| | - Cheng Hu
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
| | - Long Zhang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
| | - Haijun Jiang
- College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; School of Mathematics and Statistics, Yili Normal University, Yining 835000, China
| |
Collapse
|
2
|
Bao Y, Zhang Y, Zhang B. Resilient fixed-time stabilization of switched neural networks subjected to impulsive deception attacks. Neural Netw 2023; 163:312-326. [PMID: 37094518 DOI: 10.1016/j.neunet.2023.04.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2022] [Revised: 02/25/2023] [Accepted: 04/02/2023] [Indexed: 04/26/2023]
Abstract
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.
Collapse
Affiliation(s)
- Yuangui Bao
- School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China; School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, People's Republic of China; Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing 314000, People's Republic of China.
| | - Yijun Zhang
- School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China.
| | - Baoyong Zhang
- School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China.
| |
Collapse
|
3
|
Tai W, Li X, Zhou J, Arik S. Asynchronous dissipative stabilization for stochastic Markov-switching neural networks with completely- and incompletely-known transition rates. Neural Netw 2023; 161:55-64. [PMID: 36736000 DOI: 10.1016/j.neunet.2023.01.039] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Revised: 12/15/2022] [Accepted: 01/24/2023] [Indexed: 02/04/2023]
Abstract
The asynchronous dissipative stabilization for stochastic Markov-switching neural networks (SMSNNs) is investigated. The aim is to design an output-feedback controller with inconsistent mode switching to ensure that the SMSNN is stochastically stable with extended dissipativity. Two situations, which involve completely- and incompletely-known transition rates (TRs), are taken into account. The situation that all TRs are exactly known is considered first. By applying a mode-dependent Lyapunov-Krasovskii functional, Dynkin's formula, and several matrix inequalities, a criterion for the desired performance of the closed-loop SMSNN is derived and a design method for determining the asynchronous controller is developed. Then, the study is generalized to the situation where some TRs are allowed to be uncertain or even fully unknown. An inequality is established for judging the upper bound of the product of the TRs with the Lyapunov matrix by making full use of accessible information on the incompletely-known TRs. Based on the inequality, performance analysis and control synthesis are presented without imposing the zero-sum hypothesis of the uncertainties in the TR matrix. Finally, an example with numerical calculation and simulation is provided to verify the validity of the stabilizing approaches.
Collapse
Affiliation(s)
- Weipeng Tai
- Research Institute of Information Technology, Anhui University of Technology, Ma'anshan, 243000, Anhui, China; School of Computer Science & Technology, Anhui University of Technology, Ma'anshan, 243032, Anhui, China
| | - Xinling Li
- Research Institute of Information Technology, Anhui University of Technology, Ma'anshan, 243000, Anhui, China
| | - Jianping Zhou
- School of Computer Science & Technology, Anhui University of Technology, Ma'anshan, 243032, Anhui, China
| | - Sabri Arik
- Department of Computer Engineering, Faculty of Engineering, Istanbul University-Cerrahpasa, Istanbul, 34320, Turkey.
| |
Collapse
|
4
|
Jin Y, Kwon W, Lee S. Parameterized Luenberger-Type H ∞ State Estimator for Delayed Static Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022; 33:2791-2800. [PMID: 33406045 DOI: 10.1109/tnnls.2020.3045146] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
This article proposes a new Luenberger-type state estimator that has parameterized observer gains dependent on the activation function, to improve the H∞ state estimation performance of the static neural networks with time-varying delay. The nonlinearity of the activation function has a significant impact on stability analysis and robustness/performance. In the proposed state estimator, a parameter-dependent estimator gain is reconstructed by using the properties of the sector nonlinearity of the activation functions that are represented as linear combinations of weighting parameters. In the reformulated form, the constraints of the parameters for the activation function are considered in terms of linear matrix inequalities. Based on the Lyapunov-Krasovskii function and the improved reciprocally convex inequality, enhanced conditions for designing a new state estimator that guarantees H∞ performance are derived through a parameterization technique. The compared results with recent studies demonstrate the superiority and effectiveness of the presented method.
Collapse
|
5
|
Qian W, Shi H, Wu Z, Zhao Y. The combined functional approach to state estimation of delayed static neural network. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.01.054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
6
|
Dai J, Li Y, Xiao L, Jia L, Liao Q, Li J. Comprehensive study on complex-valued ZNN models activated by novel nonlinear functions for dynamic complex linear equations. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2020.12.078] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
7
|
Finite-time cluster synchronization in complex-variable networks with fractional-order and nonlinear coupling. Neural Netw 2021; 135:212-224. [PMID: 33421899 DOI: 10.1016/j.neunet.2020.12.015] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Revised: 10/31/2020] [Accepted: 12/14/2020] [Indexed: 11/22/2022]
Abstract
This paper is primarily concentrated on finite-time cluster synchronization of fractional-order complex-variable networks with nonlinear coupling by utilizing the non-decomposition method. Firstly, two control strategies are designed which are relevant to complex-valued sign functions. Thereafter, by employing fractional-order stability theory and complex function theory, several criteria are deduced to ensure finite-time cluster synchronization under the framework within a new norm consisting of absolute values for real and imaginary components. Furthermore, the setting time is effectively estimated based on some significant properties of fractional-order Caputo derivation and Mittag-Leffler functions. Lastly, two numerical examples are given to verify the effectiveness of theoretical results.
Collapse
|
8
|
Wu S, Han X, Li X. $$H_{\infty }$$ State Estimation of Static Neural Networks with Mixed Delay. Neural Process Lett 2020. [DOI: 10.1007/s11063-019-10171-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
9
|
Faydasicok O. New criteria for global stability of neutral-type Cohen-Grossberg neural networks with multiple delays. Neural Netw 2020; 125:330-337. [PMID: 32172142 DOI: 10.1016/j.neunet.2020.02.020] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Revised: 02/13/2020] [Accepted: 02/27/2020] [Indexed: 11/29/2022]
Abstract
The significant contribution of this paper is the addressing the stability issue of neutral-type Cohen-Grossberg neural networks possessing multiple time delays in the states of the neurons and multiple neutral delays in time derivative of states of the neurons. By making the use of a novel and enhanced Lyapunov functional, some new sufficient stability criteria are presented for this model of neutral-type neural systems. The obtained stability conditions are completely dependent of the parameters of the neural system and independent of time delays and neutral delays. A constructive numerical example is presented for the sake of proving the key advantages of the proposed stability results over the previously reported corresponding stability criteria for Cohen-Grossberg neural networks of neutral type. Since, stability analysis of Cohen-Grossberg neural networks involving multiple time delays and multiple neutral delays is a difficult problem to overcome, the investigations of the stability conditions of the neutral-type the stability analysis of this class of neural network models have not been given much attention. Therefore, the stability criteria derived in this work can be evaluated as a valuable contribution to the stability analysis of neutral-type Cohen-Grossberg neural systems involving multiple delays.
Collapse
Affiliation(s)
- Ozlem Faydasicok
- Department of Mathematics, Faculty of Science, Istanbul University, Vezneciler, Istanbul, Turkey.
| |
Collapse
|
10
|
He J, Liang Y, Yang F, Yang F. New H ∞ state estimation criteria of delayed static neural networks via the Lyapunov-Krasovskii functional with negative definite terms. Neural Netw 2020; 123:236-247. [PMID: 31887684 DOI: 10.1016/j.neunet.2019.12.008] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2019] [Revised: 10/13/2019] [Accepted: 12/10/2019] [Indexed: 10/25/2022]
Abstract
In the estimation problem for delayed static neural networks (SNNs), constructing a proper Lyapunov-Krasovskii functional (LKF) is crucial for deriving less conservative estimation criteria. In this paper, a delay-product-type LKF with negative definite terms is proposed. Based on the third-order Bessel-Legendre (B-L) integral inequality and mixed convex combination approaches, a less conservative estimator design criterion is derived. Furthermore, the desired estimator gain matrices and the H∞ performance index are obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.
Collapse
Affiliation(s)
- Jing He
- School of Automation, Northwestern Polytechnical University, Xi'an, PR China; Key Laboratory of Information Fusion Technology, Ministry of Education, Xi'an, PR China
| | - Yan Liang
- School of Automation, Northwestern Polytechnical University, Xi'an, PR China; Key Laboratory of Information Fusion Technology, Ministry of Education, Xi'an, PR China.
| | - Feisheng Yang
- School of Automation, Northwestern Polytechnical University, Xi'an, PR China; Key Laboratory of Information Fusion Technology, Ministry of Education, Xi'an, PR China
| | - Feng Yang
- School of Automation, Northwestern Polytechnical University, Xi'an, PR China; Key Laboratory of Information Fusion Technology, Ministry of Education, Xi'an, PR China
| |
Collapse
|
11
|
Further improved results on non-fragile H∞ performance state estimation for delayed static neural networks. Neurocomputing 2019. [DOI: 10.1016/j.neucom.2019.04.034] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
12
|
Wei T, Lin P, Wang Y, Wang L. Stability of stochastic impulsive reaction–diffusion neural networks with S-type distributed delays and its application to image encryption. Neural Netw 2019; 116:35-45. [DOI: 10.1016/j.neunet.2019.03.016] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2018] [Revised: 01/31/2019] [Accepted: 03/22/2019] [Indexed: 11/30/2022]
|
13
|
New stability results for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with multiple delays. Neural Netw 2019; 114:60-66. [DOI: 10.1016/j.neunet.2019.02.010] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2019] [Revised: 02/21/2019] [Accepted: 02/28/2019] [Indexed: 11/21/2022]
|
14
|
Memory-based State Estimation of T–S Fuzzy Markov Jump Delayed Neural Networks with Reaction–Diffusion Terms. Neural Process Lett 2019. [DOI: 10.1007/s11063-019-10026-8] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
15
|
Selvaraj P, Kwon OM, Sakthivel R. Disturbance and uncertainty rejection performance for fractional-order complex dynamical networks. Neural Netw 2019; 112:73-84. [PMID: 30753964 DOI: 10.1016/j.neunet.2019.01.009] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2018] [Revised: 12/02/2018] [Accepted: 01/21/2019] [Indexed: 11/30/2022]
Abstract
This paper investigates the synchronization issue for a family of time-delayed fractional-order complex dynamical networks (FCDNs) with time delay, unknown bounded uncertainty and disturbance. A novel fractional uncertainty and disturbance estimator (FUDE) based feedback control strategy is proposed to not only synchronize the considered FCDNs but also guaranteeing the precise rejection of unmodelled system uncertainty and external disturbance. Especially, in FUDE-based approach, model uncertainties and external disturbance are integrated as a lumped disturbance and it does not require a completely known system model or a disturbance model. On the other hand, the design algorithm for the proposed control strategy is based on the state-space framework, rather than frequency-based design methodologies in the literature, which helps for predominant comprehension of the inner system behaviour. Also, by the temperance of Lyapunov stability theory and fractional calculus, a set of adequate conditions in the linear matrix inequality framework is obtained, which guarantees the robust synchronization of the closed-loop system. Furthermore, an iterative optimization algorithm is proposed to improve control robustness against the external disturbance and model uncertainties. Finally, two numerical illustrations including financial network model, where the influence of adjustment of macro-economic policies in the entire financial system are given to exhibit the rightness and important features of the acquired theoretical results.
Collapse
Affiliation(s)
- P Selvaraj
- School of Electrical Engineering, Chungbuk National University, 1 Chungdao-ro, Cheongju 28644, South Korea
| | - O M Kwon
- School of Electrical Engineering, Chungbuk National University, 1 Chungdao-ro, Cheongju 28644, South Korea.
| | - R Sakthivel
- Department of Applied Mathematics, Bharathiar University, Coimbatore 641046, India; Department of Mathematics, Sungkyunkwan University, Suwon 16419, South Korea.
| |
Collapse
|
16
|
Orman Z. An improved stability result for delayed Takagi-Sugeno fuzzy Cohen-Grossberg neural networks. Neural Netw 2018; 108:445-451. [PMID: 30312960 DOI: 10.1016/j.neunet.2018.09.008] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2018] [Revised: 08/31/2018] [Accepted: 09/14/2018] [Indexed: 11/28/2022]
Abstract
This work proposes a novel and improved delay independent global asymptotic stability criterion for delayed Takagi-Sugeno (T-S) fuzzy Cohen-Grossberg neural networks exploiting a suitable fuzzy-type Lyapunov functional in the presence of the nondecreasing activation functions having bounded slopes. The proposed stability criterion can be easily validated as it is completely expressed in terms of the system matrices of the fuzzy neural network model considered. It will be shown that the stability criterion obtained in this work for this type of fuzzy neural networks improves and generalizes some of the previously published stability results. A constructive numerical example is also given to support the proposed theoretical results.
Collapse
Affiliation(s)
- Zeynep Orman
- Department of Computer Engineering, Faculty of Engineering, Istanbul University-Cerrahpasa, 34320 Avcilar, Istanbul, Turkey.
| |
Collapse
|