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一类分数阶时滞微分系统的精确解及Hyers-Ulam稳定性

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东华大学学报（自然科学版） 2024年第1期50卷 152-162页

作者：邬忆萱寇春海东华大学理学院上海201620

为拓展整数阶微分系统的已有结果,研究了一类具有多个时滞的Caputo分数阶线性微分系统。运用不可交换矩阵的多项式定理,在不要求系数矩阵可交换的前提下,得到了系统的精确解表示。研究结果表明,该系统在有限时间内Hyers-Ulam稳定。

关键词：时滞系统 Hyers-Ulam稳定 Laplace变换 Caputo分数阶导数不可交换矩阵精确解

Cyber-Physical Systems as General Distributed Parameter Systems:Three Types of Fractional Order Models and Emerging Research Opportunities

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IEEE/CAA Journal of Automatica Sinica 2015年第4期2卷 353-357页

作者： Fudong Ge YangQuan Chen chunhai kou College of Information Science and Technology Donghua University Mechatronics Embedded Systems and Automation Lab University of California Department of Applied Mathematics Donghua University

Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks. © 2014 Chinese Association of Automation.

关键词： Laplace equation Laplace transforms Mathematical operators

Finite-Time Stability for Nonlinear Fractional Differential Equations with Time Delay

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Journal of Donghua University(English Edition) 2022年第5期39卷 446-453页

作者： HE Huazhen kou chunhai College of Science Donghua UniversityShanghai 201620China

The finite-time stability and the finite-time contractive stability of solutions for nonlinear fractional differential equations with bounded delay are investigated. The derivative of Lyapunov function along solutions of the considered system is defined in terms of the Caputo fractional Dini derivative. Based on the Lyapunov-Razumikhin method, several sufficient criteria are established to guarantee the finite-time stability and the finite-time contractive stability of solutions for the related systems. An example is provided to illustrate the effectiveness of the obtained results.

关键词： finite-time stability nonlinear fractional differential equation time delay Caputo fractional Dini derivative Lyapunov-Razumikhin method

Adaptive Control and Synchronization for a Class of Nonlinear Fractional Order Systems with Uncertainty

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Journal of Donghua University(English Edition) 2019年第4期36卷 405-412页

作者： LEI Huajing kou chunhai CAI Ruiyang HE Binbin College of Science Donghua UniversityShanghai 201620China College of Information Science and Technology Donghua UniversityShanghai 201620China College of Urban Railway Transportation Shanghai University of Engineering ScienceShanghai 201620China

This paper investigates the design of adaptive control for a class of nonlinear fractional order systems with multiple unknown *** using the adaptive backstepping method and fractional Lyapunov method,an adaptive feedback controller is proposed to stabilize the closed-loop *** parameter estimation adaptive law is also ***,these results are applied to the master-slave configuration synchronization of the studied ***,numerical simulation is provided to demonstrate the effectiveness of our results.

关键词： adaptive control synchronization backstepping method fractional order system uncertainty

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEM

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Annals of Differential Equations 2006年第3期22卷 467-472页

作者： Zhang Xiuyun kou chunhai (Dept. of Applied Math., Donghua University, Shanghai 201620)

In this paper we prove the existence and uniqueness of the solution for a class of nonlinear fractional differential system, and investigate the dependence of the solution on the orderαi.

关键词： Riemann-Liouville fractional derivative/integral fractional differential equations existence uniqueness dependence

一类非瞬时脉冲微分系统的Ulam型稳定性分析

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东华大学学报（自然科学版） 2023年第1期49卷 126-133页

作者：王瑞寇春海东华大学理学院上海201620

针对一类非瞬时脉冲微分系统,研究其解的存在性和Ulam型稳定性,构造上下解的迭代序列,得到系统的最小解和最大解。基于上下解方法,在标量情形下给出了此类系统Ulam型稳定的充分条件,以一个算例验证所得结论的有效性。

关键词：非瞬时脉冲微分系统 Ulam型稳定性上下解方法时滞存在性

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基于观测器的不确定再入飞行器模型的控制

东华大学学报（自然科学版） 2017年第5期43卷 764-770页

作者：杨夫猛寇春海东华大学理学院上海201620

利用Lyapunov稳定性理论并结合LMI(linear matrix inequation)方法,基于状态观测器,研究了一类含有不确定时变参数的再入飞行器模型的控制问题.首先,验证了观测器的可行性.其次,基于观测器设计了状态反馈控制器,以保证系统的稳定性.最后... 详细信息

利用Lyapunov稳定性理论并结合LMI(linear matrix inequation)方法,基于状态观测器,研究了一类含有不确定时变参数的再入飞行器模型的控制问题.首先,验证了观测器的可行性.其次,基于观测器设计了状态反馈控制器,以保证系统的稳定性.最后,给出一个再入飞行器模型的实例仿真以验证新提出的方法的有效性.

关键词：再入飞行器状态观测器控制器稳定性

带有时滞的分数阶神经网络的有限时间稳定性分析

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延边大学学报（自然科学版） 2013年第2期39卷 88-92页

作者：宋扬寇春海东华大学理学院上海201620

研究具有时滞的分数阶神经网络模型CDαui(t)=-diui(t)+Σnj=1aijgj(uj(t))+Σnj=1bijfj(uj(t-τj))+Ii,i=1,2,…,n的有限时间稳定性.通过Bellman-Gronwall不等式和Bihari不等式得到了该模型满足有限时间稳定的充分条件,并通过两个例子... 详细信息

关键词：分数阶神经网络有限时间稳定

C_h空间中无穷时滞随机泛函微分方程解的存在唯一性

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应用数学与计算数学学报 2016年第2期30卷 260-271页

作者：李毓媛寇春海东华大学信息科学与技术学院上海201620 东华大学理学院上海201620

研究了一类具有无穷时滞的随机泛函微分方程,以空间(C_h,|·|_h)为相空间,利用Picard迭代法,借助于Bihari不等式,得到了系数在满足非Lipschitz条件和弱化的线性增长条件时解的存在唯一性.

关键词：随机泛函微分方程无穷时滞 C_h空间存在性唯一性