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Finite-time stability of solutions for non-instantaneous impulsive systems and application to neural networks

NEUROCOMPUTING 2023年 537卷 1-11页

作者： Deng, Hao Li, Chuandong Wang, Yinuo Wu, Hongjuan Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

This work extends the finite-time stability (FTS) results to non-instantaneous impulsive time-varying systems on the basis of general impulsive systems via Lyapunov theory. The impacts of impulse numbers, impulse time sequences and impulse amplitudes on FTS and settling-time estimation are discussed. The effects of different types of impulses on settling-time are discussed when the impulse number is known or pre-given. The average impulsive interval is introduced to extend the above results to the case when the impulse number is unknown, and the derivative of Lyapunov function is allowed to be indefinite instead of being negative definite or semi-negative definite. Moreover, the theoretical results are applied to non-instantaneous impulsive neural networks. Finally, we provide two numerical examples to demon-strate the effectiveness and feasibility of the obtained results.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Finite-time stability Settling-time Lyapunov theory Non-instantaneous impulsive neural networks Average impulsive interval

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Synchronization issue of coupled neural networks based on flexible impulse control

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NEURAL NETWORKS 2022年第0期149卷 57-65页

作者： Xiu, Ruihong Zhang, Wei Zhou, Zichuan Southwest Univ Dept Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

The global exponential synchronization issue of coupled neural networks with time-delayed impulses is investigated in this paper. On the basis of the characteristics of coupled neural networks and theorems, we have built a novel coupled systems model. In order to fit the real situation, the impulses are flexible and it can beyond the impulsive interval under certain conditions in this paper. Therefore, our results are less restrictive and more practical compared to existing research. Besides, by using average impulsive delay (AID) and average impulsive interval (AII), we investigate two different effects of impulses on synchronization respectively and get a few adequate conditions for different types of synchronization. Finally, there are two examples of numerical simulations presented to illustrate the efficiency of the conclusions.

关键词： Global exponential synchronization Average impulsive interval Average impulsive delay Neural networks

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Asymptotic stability of non-instantaneous impulsive systems and T-S fuzzy non-instantaneous impulsive control for nonlinear systems

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IET CONTROL THEORY AND APPLICATIONS 2023年第9期17卷 1184-1202页

作者： Deng, Hao Li, Chuandong Wang, Yinuo Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

This paper studies the asymptotic stability for a class of non-instantaneous impulsive systems and Takagi-Sugeno (T-S) fuzzy non-instantaneous impulsive control for linear and nonlinear systems. First, a class of concrete comparison system for a more accurate and universal nonlinear non-instantaneous impulsive model is constructed. Then, the less conservative sufficient conditions of Lyapunov asymptotic stability are studied by impulsive differential inequalities and generalized comparison principle. On the other hand, an improved non-instantaneous impulsive control scheme with T-S fuzzy model is also presented for the asymptotic stability of the nonlinear systems. Finally, simulation results on controlling a linear and a nonlinear system are presented to illustrate the rationality and effectiveness of the obtained results.

关键词： asymptotic stability fuzzy control nonlinear dynamical systems

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Mean-square stabilization of impulsive neural networks with mixed delays by non-fragile feedback involving random uncertainties

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NEURAL NETWORKS 2022年第0期154卷 469-480页

作者： Zhang, Xiaoyu Li, Chuandong Li, Hongfei Cao, Zhengran Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

In this paper, we consider a class of neural networks with mixed delays and impulsive interferences. Firstly, a sufficient condition is given to ensure the existence and uniqueness of the equilibrium point of the proposed neural networks by employing the contraction mapping theorem. Secondly, we discuss the issue of the exponential stability in mean-square of the equilibrium point by a non -fragilely delayed output coupling feedback which involves stochastically occurring gain oscillations. The designed feedback input can be tolerant of limited stochastic fluctuations of control gains and be robust against potential errors caused by factors like round-off. By combining methods of Lyapunov- Krasovskii functional and free-weighting matrix, a delay-dependent output coupling feedback with stochastically occurring uncertainties is designed and linear-matrix-inequalities(LMIs)-based sufficient conditions for the exponential stabilization in mean square are derived. Finally, three numerical examples are presented to illustrate the feasibility of theoretical results with a benchmark real-world problem. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： Non-fragile feedback Distributed delay Lyapunov-Krasovskii functional LMIs Mean-square stability

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Event-Triggered Containment Control for nonlinear Multiagent Systems via Reinforcement Learning

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IEEE TRANSACTIONS ON circuits AND SYSTEMS II-EXPRESS BRIEFS 2023年第8期70卷 2904-2908页

作者： Wang, Zichen Wang, Xin Zhao, Chen Southwest Univ Coll Westa Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

Herein, we concern with the problem of event-triggered containment optimal control for a class of nonlinear multiagent discrete-time systems (MADSs). Compared to the previous containment control strategy for linear MADSs, a novel containment control strategy for nonlinear MADSs via the backstepping technique is introduced. Utilizing the classic reinforcement learning (RL) approach, we implement the ${n}$ -step backstepping structure with actor-critic neural networks (NNs). In addition, instead of a time-triggered scheme, the event-triggered scheme (ETS) is employed for saving computations. Finally, some simulation results are presented to verify the performance of our control strategy.

关键词： Containment control event-triggered reinforcement learning nonlinear multiagent systems

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Design of Controllers for Finite-Time Robust Stabilization of Inertial Delayed Neural Networks with External Disturbances

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NEURAL PROCESSING LETTERS 2023年第7期55卷 9387-9408页

作者： Hong, Nan Zhang, Wei Zhou, Zichuan Xiu, Ruihong Southwest Univ Dept Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

This paper studies the problem of finite-time robust stabilization of inertial delayed neural networks with external disturbances. The finite-time stability research of inertial neural networks can be applied to important fields such as secure communication, so it has great significant research value. However, up to now, there are few previous studies on the finite time stability of inertial neural networks, thus this paper makes up for this gap. Based on the actual communication networks, we improve the model of inertial neural networks, adding uncertainties and external disturbances. Unlike many previous papers based on scalar sign function, this paper introduces vector sign function, combines the constructed Lyapunov function, some inequality conditions, and related lemmas to design two effective controllers composed of U1(t) and U2(t), which can handle uncertainties and external disturbances of the neural networks well, and realize finite-time robust stability of the neural networks with external disturbances. In addition, the theoretical part of this paper estimates an upper bound on the settling time for the system to reach stability. Under the conditions of a certain strategy, we further optimize the extremes of the settling time so that the system reaches stability in a shorter time. Our results improve and extend some recent works. Finally, two examples are given to verify the validity and correctness of the designed controllers by numerical simulations using MATlab tool.

关键词： Time-delay Inertial neural networks Finite-time robust stabilization Settling time External disturbances

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A class of adaptive filtering algorithms based on improper complex correntropy

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informatION SCIENCES 2023年 633卷 573-596页

作者： Qian, Guobing Yu, Xin Mei, Jiaojiao Liu, Junzhu Wang, Shiyuan Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

As a robust online learning approach, adaptive filtering based on correntropy has attracted more attentions. Recently, researchers have made efforts to develop complex correntropy to deal with adaptive filtering issues in complex domain. However, most of the literature on complex cor-rentropy lack details regarding the processing of noncircular signals. Up to now, the maximum improper complex correntropy criterion (MICCC) algorithm for noncircular and widely-linear (WL) adaptive filtering utilizes the gradient descent method to find the maximum of the objec-tive function. However, the MICCC algorithm fails to guarantee both low steady-state weight error power and fast convergence. To overcome this defect, this paper proposes a class of adaptive filtering algorithms which are based on fixed-point instead of gradient descent. It is worth noting that we manage to avoid the massive calculation of matrix inversion in traditional fixed-point based methods by utilizing the lemma of matrix inversion properly and further provide two alternative recursive algorithms. Finally, the local convergence analysis of mean and mean square is performed, and the simulated results offer strong evidences for the superior performance of the proposed algorithms over widely-linear complex least mean square (WL-CLMS), widely-linear recursive least square (WL-RLS) and MICCC.

关键词： Online learning Fixed-point Adaptive filter Improper complex correntropy Widely linear Convergence analysis

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Bipartite synchronization of Lur?e network with signed graphs based on intermittent control

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ISA TRANSACTIONS 2023年 135卷 290-298页

作者： Yang, Jinyue Huang, Junjian He, Xing Yang, Wenqiang Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

In this paper, the bipartite synchronization of signed Lur'e network is studied under intermittent control, where the communication relationship of these adjacent nodes in the network can be either cooperative or competitive. Assuming that the network is structurally balanced, bipartite synchronization can be reached with some conditions and coordinate transform criterion. Then, Based on Lyapunov stability theory, some important norms are established. Ultimately, the simulation results can illustrate validness of theoretical analysis. (c) 2022 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Bipartite synchronization Lur?e network Signed graphs Intermittent control Leader-following synchronization

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Global μ-synchronization for coupling delayed complex dynamical networks via event-triggered delayed impulsive control

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ISA TRANSACTIONS 2024年 145卷 124-131页

作者： Zhang, Wei Xiao, Jun Gong, Bingyan Southwest Univ Dept Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

This paper mainly focuses on solving the global mu-synchronization issue of complex dynamical networks (CDNs) by a novel event-triggered impulsive control (ETIC) method with time delays. This method combines the advantages of impulsive control and event-triggered control and gets rid of the limitation that the Lyapunov function decreases strictly monotonically with the sequence of event triggers. An event-triggered mechanism is specifically designed to realize mu-synchronization for CDNs in this paper, which means that event-triggered control has been applied to mu-synchronization field for the first time. Compared with periodic impulsive control, ETIC only produces control effects when the event-triggered mechanism are met, which is more in line with the actual situation. By Lyapunov-Razumikhin, recursion, etc, some valid global mu-synchronization criteria of CDNs are obtained and also Zeno behavior is avoided. Additionally, coupled delays and uncertainties are considered in CDNs. Finally, two numerical examples are shown to demonstrate the correctness of the designed ETIC strategy.

关键词： Parametric uncertainty nonlinear complex dynamical networks Time delay mu-synchronization Event-triggered control

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Impulsive Projection Neural Networks for Variational Inequalities and Sparse Signal Reconstruction Application

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COGNITIVE COMPUTATION 2024年第3期16卷 877-887页

作者： Xu, Jing Li, Chuandong He, Xing Wen, Hongsong Southwest Univ Coll Elect & Informat Engn Chongqing Key Lab Nonlinear Circuits & Intelligent Chongqing 400715 Peoples R China

Variational inequalities (VIs) have become a general framework for efficient problems in various fields such as optimal control and nonlinear programming. Some real problems in application areas such as signal processing and network resource allocation can be transformed into VIs. VIs have been frequently solved using neurodynamic approaches, which have good performance and low computational cost. In this paper, two novel projection neural networks (PNNs) with impulsive effects are presented to deal with VIs. Based on the impulsive system theory and PNN, an impulsive projection neural network (IPNN) and its modified version are proposed. Then the stability properties of the presented IPNN and modified impulsive projection neural network (MIPNN) are analyzed by Lyapunov functions and impulsive system theory. VIs can be addressed with the proposed IPNN and MIPNN. Furthermore, two PNNs are applied to sparse signal reconstruction. It is also shown that the solutions of the proposed IPNN and MIPNN converge to the solution of the corresponding VIs. Meanwhile, sparse signals can also be accurately reconstructed by IPNN and MIPNN. Compared with the classical neural network, the newly designed IPNN and MIPNN have an improvement in the convergence rates because of the introduction of impulsive effects. Theoretical results and simulations show the effectiveness and feasibility of the IPNN and MIPNN.

关键词： Projection Neural Networks (PNNs) Impulsive effect Variational Inequalities (VIs) Sparse signal reconstruction

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