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Global exponential stability of almost periodic solution for a large class of delayed dynamical systems

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Science China Mathematics 2005年第8期48卷 1015-1026页

作者： lu wenlian CHEN Tianping Key Laboratory of Nonlinear Mathematics Science of Ministry of Education Fudan University Shanghai200433 China Key Laboratory of Nonlinear Mathematics Science of Ministry of Education Fudan University Shanghai200433 China

Research on delayed neural networks with variable self-inhibitions, interconnection weights, and inputs is an important issue. In this paper, we discuss a large class of delayed dynamical systems with almost periodic self-inhibitions, inter-connection weights, and inputs. This model is universal and includes delayed systems with timevarying delays, distributed delays as well as combination of both. We prove that under some mild conditions, the system has a unique almost periodic solution, which is globally exponentially stable. We propose a new approach, which is independent of existing theory concerning with existence of almost periodic solution for dynamical systems.

关键词： delayed dynamical systems almost penodic solution global exponential convergence

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Human brain computing and brain-inspired intelligence

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National Science Review 2024年第5期11卷 8-9页

作者： Jianfeng Feng Viktor Jirsa wenlian lu Institute of Science and Technology for Brain-Inspired Intelligence Fudan University Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence(Fudan University) Ministry of Education Shanghai Center for Mathematical Sciences Fudan University Department of Computer Science University of Warwick Zhangjiang Fudan International Innovation Center Institut de Neurosciences des Systèmes Faculté de Medécine

The relationship between structure, neural activity dynamics and intelligent human brain function is complex and multifaceted with deep roots in several academic disciplines. Its understanding is a fundamental goal of brain research [1] and may indicate the way towards the next generation of artificial intelligence [2]. There are major challenges on the way, several of which are addressed in this Special Topic of National Science Review.

关键词： intelligence human brain-inspired computing

Using Event-Based Method to Estimate Cybersecurity Equilibrium

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IEEE/CAA Journal of Automatica Sinica 2021年第2期8卷 455-467页

作者： Zhaofeng Liu Ren Zheng wenlian lu Shouhuai Xu the School of Mathematical Sciences Fudan UniversityShanghai 200433China the Artificial Intelligence Laboratory SAIC Motor Corporation LimitedShanghai 200041 SAIC Intelligent Technology(Shanghai)Corporation Limited Shanghai 200433China the School of Mathematical Sciences Fudan Universityand Shanghai Center for Mathematical SciencesFudan Universityand also with Shanghai Key Laboratory for Contemporary Applied MathematicsShanghai 200433China the Department of Computer Science University of Texas at San AntonioSan Antonio TX 78249 USA

Estimating the global state of a networked system is an important problem in many application *** classical approach to tackling this problem is the periodic(observation)method,which is inefficient because it often observes states at a very high *** inefficiency has motivated the idea of event-based method,which leverages the evolution dynamics in question and makes observations only when some rules are triggered(i.e.,only when certain conditions hold).This paper initiates the investigation of using the event-based method to estimate the equilibrium in the new application domain of cybersecurity,where equilibrium is an important metric that has no closed-form *** specifically,the paper presents an event-based method for estimating cybersecurity equilibrium in the preventive and reactive cyber defense dynamics,which has been proven globally *** presented study proves that the estimated equilibrium from our trigger rule i)indeed converges to the equilibrium of the dynamics and ii)is Zeno-free,which assures the usefulness of the event-based *** examples show that the event-based method can reduce 98%of the observation cost incurred by the periodic *** order to use the event-based method in practice,this paper investigates how to bridge the gap between i)the continuous state in the dynamics model,which is dubbed probability-state because it measures the probability that a node is in the secure or compromised state,and ii)the discrete state that is often encountered in practice,dubbed sample-state because it is sampled from some *** bridge may be of independent value because probability-state models have been widely used to approximate exponentially-many discrete state systems.

关键词： Cybersecurity dynamics cybersecurity equilibrium event-based method global state estimation preventive and reactive cyber defense dynamics

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Finite-time synchronization for nonlinear multi-agent system with directed structure by iterative learning control 36

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Finite-time synchronization for nonlinear multi-agent system...

第36届中国控制会议

作者： Zongzong Lin Tianping Chen wenlian lu School of Mathematical Science Fudan University School of Computer Science Fudan University

ISBN: (纸本)9781538629185

In this paper,we study the iterative learning control（ILC） method for nonlinear multi-agent system（MAS） to reach finite-time synchronization under the directed communication *** propose the distributed D-type iterative learning control for system whose nonlinear function satisfies the global lipschitz continuous when the graph has a spinning *** choosing the parameter γ∈[0,1],the y-adaptive iterative learning control rule（γ-AILC） can deal with the case of identical initial condition or alignment *** the end,Simulations are provided to illustrate the results.

关键词： Synchronization Iterative learning control Multi-agent system Directed structure

Cluster consensus of networks of second-order multi-agent systems with inter-cluster non-identical inputs

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Cluster consensus of networks of second-order multi-agent sy...

第25届中国控制与决策会议

作者： Yujuan Han wenlian lu Tianping Chen School of Mathematical Sciences Fudan University Centre for Computational Systems Biology Fudan University School of Computer Science Fudan University

ISBN: (纸本)9781467355339

This paper studies the second order cluster consensus problem for a network of multi-agents. We consider general graph topologies including time variation. A comprehensive analysis is provided. For static topology case, we show that communications among agents and inter-cluster nonidentical inputs generically leads the system to second order cluster consensus. A common Lyapunov function is provided for time varying topologies case. Numerical simulation results demonstrate that the second order cluster consensus can be achieved using the proposed algorithms.

关键词： cluster consensus second-order dynamical system inter-cluster non-identical inputs

On Second-order Synchronization Protocols of Multi-agent Systems 36

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On Second-order Synchronization Protocols of Multi-agent Sys...

第36届中国控制会议

作者： Junya Chen Tianping Chen wenlian lu School of Mathematical Sciences Fudan University School of Computer Science Fudan University Institute of Science and Technology for Brain-Inspired Intelligence Fudan University

ISBN: (纸本)9781538629185

In this paper,an approach is proposed to design synchronization protocols for a network of second-order *** prove a series of sufficient conditions for different asymptotic coordination dynamics including synchronization,consensus and *** conditions are rather general,which can include some existing results as *** addition,we can employ them to construct novel second-order synchronization *** present numerical examples to illustrate the efficiency of the theoretical results.

关键词： Synchronization Consensus Second-order multiagent systems Matrix equation Stability

Synchronization analysis of coupled differential systems with time-varying couplings

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Synchronization analysis of coupled differential systems wit...

第25届中国控制与决策会议

作者： Xinlei Yi wenlian lu Tianping Chen School of Mathematical Sciences Fudan University Centre for Computational Systems Biology Fudan University School of Computer Science Fudan University

ISBN: (纸本)9781467355339

This paper considers the problem of synchronization of differential dynamical systems with time-varying coupling. The temporal variation of the couplings we consider here is rather general and includes variations in both the network structure and the reaction dynamics. For example, driven by a metric dynamical system. Inspired by the author’s previous work [1], the generalized Hajnal diameter is introduced to study the stability of synchronization manifold via the underlying variational equation, which can be proved to equal to eλ , whereλ is the largest one of all Lyapunov exponents of the underlying variational equation, corresponding to the space transverses to the synchronization manifold. As an application, these results are used to investigate the synchronization of linearly coupled ordinary differential systems （LCODEs） with identity inner coupling matrix. In this case, the Hajnal diameter of the linear system induced by the time-varying coupling matrices can be used to measure the synchronizability of the time-varying coupling process. The corresponding network can synchronize some chaotic attractors if and only if there exists some T ＞ 0 such that the joint union of the topologies across any T -length time interval has spanning trees.

关键词： Linearly coupled ordinary equations time-varying coupling synchronization Hajnal diameter Lyapunov exponents

A New Approach to Synchronization Analysis of Linearly Coupled Map Lattices

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Chinese Annals of Mathematics,Series B 2007年第2期28卷 149-160页

作者： wenlian lu Tianping CHENt Published online March School of Mathematical Sciences and Laboratory of Mathematics for Nonlinear Sciences Fudan University Shanghai 200433 China.

In this paper, a new approach to analyze synchronization of linearly coupled map lattices （LCMLs） is presented. A reference vector x（t） is introduced as the projection of the trajectory of the coupled system on the synchronization manifold. The stability analysis of the synchronization manifold can be regarded as investigating the difference between the trajectory and the projection. By this method, some criteria are given for both local and global synchronization. These criteria indicate that the left and right eigenvectors corresponding to the eigenvalue ＂0＂ of the coupling matrix play key roles in the stability of synchronization manifold for the coupled system. Moreover, it is revealed that the stability of synchronization manifold for the coupled system is different from the stability for dynamical system in usual sense. That is, the solution of the coupled system does not converge to a certain knowable s（t） satisfying s（tT1） = f（s（t）） but to the reference vector on the synchronization manifold, which in fact is a certain weighted average of each x^i（t） for i=1,……, m, but not a solution s（t） satisfying s（t ＋ 1）=f（s（t））.

关键词： Linearly coupled map lattices Synchronization Synchronizationmanifold Local stability of synchronization manifold Global stability of synchronization manifold

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Dynamical behaviors of recurrently connected neural networks and linearly coupled networks with discontinuous right-hand sides

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Frontiers of Electrical and Electronic Engineering in China 2012年第1期7卷 32-48页

作者： wenlian lu Tianping CHEN Bo LIU Xiangnan HE School of Mathematical Sciences Fudan UniversityShanghai 200433China

The aim of this paper is to provide a sys- tematic review on the framework to analyze dynamics in recurrently connected neural networks with discontinu- ous right-hand sides with a focus on the authors＇ works in the past three years. The concept of the Filippov so- lution is employed to define the solution of the neural network systems by transforming them to differential in- clusions. The theory of viability provides a tool to study the existence and uniqueness of the solution and the Lya- punov function （functional） approach is used to investi- gate the global stability and synchronization. More pre- cisely, we prove that the diagonal-dominant conditions guarantee the existence, uniqueness, and stability of a general class of integro-differential equations with （al- most） periodic self-inhibitions, interconnection weights, inputs, and delays. This model is rather general and in- cludes the well-known Hopfield neural networks, Cohen- Grossberg neural networks, and cellular neural networks as special cases. We extend the absolute stability anal- ysis of gradient-like neural network model by relaxing the analytic constraints so that they can be employed to solve optimization problem with non-smooth cost func- tions. Furthermore, we study the global synchronization problem of a class of linearly coupled neural network with discontinuous right-hand sides.

关键词： delayed integro-differential system discontinuous activation ahnost periodic function nonsmooth cost function complete synchronization