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lyapunov function as potential function: A dynamical equivalence

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Chinese Physics B 2014年第1期23卷 136-141页

作者：袁若石马易安苑波敖平 School of Biomedical Engineering Shanghai Jiao Tong University Shanghai Center for Systems Biomedicine Shanghai Jiao Tong University Department of Applied Mathematics University of Washington Department of Computer Science and Engineering Shanghai Jiao Tong University Department of Physics Shanghai Jiao Tong University

For a physical system, regardless of time reversal symmetry, a potential function serves also as a lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for lyapunov function and suggests new approaches on the significant unsolved problem namely to construct lyapunov functions for general nonlinear systems. In addition, a connection is found that the lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.

关键词： lyapunov function potential function stochastic process generalized Einstein relation

Quantum control based on three forms of lyapunov functions

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Chinese Physics B 2024年第4期33卷 216-222页

作者：俞国慧杨洪礼 College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

This paper introduces the quantum control of lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given.

关键词： quantum system lyapunov function particle swarm optimization simulated annealing algorithms quantum control

lyapunov function-based obstacle avoidance scheme for a two-wheeled mobile robot

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控制理论与应用（英文版） 2008年第4期6卷 399-404页

作者： Akira INOUE Katsuya SEKIGUCHI Department of Systems Engineering

An obstacle avoidance scheme of a two-wheeled mobile robot is shown by selecting an appropriate Lya- punov function. When considering the obstacle, the lyapunov function may have some local minima. A method which erases the local minima is proposed by using a function which covers the minima with a plane surface. The effectiveness of the proposed method is verified by numerical simulations.

关键词： Obstacle avoidance lyapunov function Mobile robot Robot control

Command filtered integrated estimation guidance and control for strapdown missiles with circular field of view

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Defence Technology（防务技术） 2024年第5期35卷 211-221页

作者： Wei Wang Jiaqi Liu Shiyao Lin Baokui Geng Zhongjiao Shi School of Aerospace Engineering Beijing Institute of TechnologyBeijing 10081China China Research and Development Academy of Machinery Equipment Beijing 100089China Northwest Industries Group CO. Ltd.Xi'an 710043China

In this paper,an integrated estimation guidance and control(IEGC)system is designed based on the command filtered backstepping approach for circular field-of-view(FOV)strapdown missiles.The threedimensional integrated estimation guidance and control nonlinear model with limited actuator deflection angle is established considering the seeker's FOV constraint.The boundary time-varying integral barrier lyapunov function(IBLF)is employed in backstepping design to constrain the body line-of-sight(BLOS)in IEGC system to fit a circular FOV.Then,the nonlinear adaptive controller is designed to estimate the changing aerodynamic parameters.The generalized extended state observer(GESO)is designed to estimate the acceleration of the maneuvering targets and the unmatched time-varying disturbances for improving tracking accuracy.Furthermore,the command filters are used to solve the"differential expansion"problem during the backstepping design.The lyapunov theory is used to prove the stability of the overall closed-loop IEGC system.Finally,the simulation results validate the integrated system's effectiveness,achieving high accuracy strikes against maneuvering targets.

关键词： Integrated estimation guidance and control Circular field-of-view Time-varying integral barrier lyapunov function Command filtered backstepping control Nonlinear adaptive control Extended state observer

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Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

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Journal of Applied Mathematics and Physics 2024年第2期12卷 509-532页

作者： Modeste N’zi Boubacar Sidiki Kouyaté Ilimidi Yattara Modibo Diarra Laboratory of Applied Mathematics and Computer Science University Felix Houphouet-Boigny Abidjan C&#244te d’Ivoire Department of Mathematics and Computer Science University of Science Technic and Technologies Bamako Mali

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.

关键词： SIRS Delayed Epidemic Model Nonlinear Incidence rate lyapunov function Asymptotic Stability in Probability

Global Stability Analysis of the Mathematical Model for Malaria Transmission between Vector and Host Population

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American Journal of Computational Mathematics 2024年第2期14卷 275-289页

作者： Raghad Alsulami Amal Almatrafi Nehad Almohammadi Hanin Alosaimi H. A. Batarfi Department of Mathematics Faculty of Science King Abdulaziz University Jeddah Kingdom of Saudi Arabia

In this paper, we discuss a mathematical model of malaria transmission between vector and host population. We study the basic qualitative properties of the model, the boundedness and non-negativity, calculate all equilibria, and prove the global stability of them and the behaviour of the model when the basic reproduction ratio R0 is greater than one or less than one. The global stability of equilibria is established by using lyapunov method. Graphical representations of the calculated parameters and their effects on disease eradication are provided.

关键词： Malaria Transmission Global Stability lyapunov function

Stochastic stability of quasi-integrable Hamiltonian systems with time delay by using lyapunov function method

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中国科学:技术科学 2010年第2期 217-217页

作者： LING Quan1, JIN XiaoLing1 & HUANG ZhiLong2 1 Department of Mechanics, Zhejiang University, Hangzhou 310027, China 2 State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China

The asymptotic lyapunov stability of one quasi-integrable Hamiltonian system with time-delayed feedback control is studied by using lyapunov functions and stochastic averaging method. First, a quasi-integrable Hamiltonian system with time-delayed feedback control subjected to Gaussian white noise excitation is approximated by a quasi-integrable Hamiltonian system without time delay. Then, stochastic averaging method for quasi-integrable Hamiltonian system is used to reduce the dimension of the original system, and after that the lyapunov function of the averaged It? equation is taken as the optimal linear combination of the corresponding independent first integrals in involution. Finally, the stability of the system is determined by using the largest eigenvalue of the linearized system. Two examples are used to illustrate the proposed procedure and the effects of delayed time on the lyapunov stability are discussed as well.

关键词： lyapunov stability lyapunov function time delay stochastic averaging

On constructing lyapunov function for formation control of Multi-agent Systems with directed topology

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On constructing Lyapunov function for formation control of M...

Consensus analysis of discrete-time multi-agent systems in switching networks: a time-varying lyapunov function method

第32届中国控制与决策会议

作者： XIAO Zhicai QIN Liang YAN Shi QI Yahui Naval Aeronautical University

This paper considers the time-varying formation problem for Multi-agent Systems,which the communication topology is directed.Distributed consensus protocol is constructed based on relative states information of neighbor agents.Then using the full rank decomposition of the Laplacian matrix,one linear transformation is introduced to transform the formation problem into consensus problem.By constructing a proper formation error vector,the formation problem with directed topology is converted into a stabilization problem of a reduced dimensionality error system.Sufficient conditions are obtained using lyapunov approach.The new approach can relax the constraint of topology condition.Finally,numerical simulations are provided to demonstrate the effectiveness of the analytical results.

关键词： Consensus Formation control LMI lyapunov function

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Consensus analysis of discrete-time multi-agent systems in s...