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bifurcation analysis and control study of improved full-speed differential model in connected vehicle environment

Chinese Physics B 2024年第7期33卷 245-266页

作者：艾文欢雷正清李丹洋方栋梁刘大为 College of Computer Science and Engineering Northwest Normal UniversityLanzhou 730070China College of Electrical Engineering Lanzhou Institute of TechnologyLanzhou 730050China

In recent years, the traffic congestion problem has become more and more serious, and the research on traffic system control has become a new hot spot. Studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable pivots can alleviate the traffic congestion problem from a new perspective. In this work, the full-speed differential model considering the vehicle network environment is improved in order to adjust the traffic flow from the perspective of bifurcation control, the existence conditions of Hopf bifurcation and saddle-node bifurcation in the model are proved theoretically, and the stability mutation point for the stability of the transportation system is found. For the unstable bifurcation point, a nonlinear system feedback controller is designed by using Chebyshev polynomial approximation and stochastic feedback control method. The advancement, postponement, and elimination of Hopf bifurcation are achieved without changing the system equilibrium point, and the mutation behavior of the transportation system is controlled so as to alleviate the traffic congestion. The changes in the stability of complex traffic systems are explained through the bifurcation analysis, which can better capture the characteristics of the traffic flow. By adjusting the control parameters in the feedback controllers, the influence of the boundary conditions on the stability of the traffic system is adequately described, and the effects of the unstable focuses and saddle points on the system are suppressed to slow down the traffic flow. In addition, the unstable bifurcation points can be eliminated and the Hopf bifurcation can be controlled to advance, delay, and disappear,so as to realize the control of the stability behavior of the traffic system, which can help to alleviate the traffic congestion and describe the actual traffic phenomena as well.

关键词： bifurcation analysis vehicle queuing bifurcation control Hopf bifurcation

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bifurcation control FOR A FRACTIONAL-ORDER DELAYED SEIR RUMOR SPREADING MODEL WITH INCOMMENSURATE ORDERS

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Acta Mathematica Scientia 2023年第6期43卷 2662-2682页

作者：叶茂林蒋海军 College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830046China

A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is ***,Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback ***,a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the ***,in order to verify the theoretical results,some numerical simulations are given.

关键词： rumor spreading fractional-order time delay bifurcation control

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bifurcation control of a fractional-order delayed competition and cooperation model of two enterprises

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Science China(Technological Sciences) 2019年第12期62卷 2130-2143页

作者： XU ChangJin LIAO MaoXin LI PeiLuan Guizhou Key Laboratory of Economics System Simulation Guizhou University of Finance and EconomicsGuiyang 50004China School of Mathematics and Physics University of Souh ChinaHengyang 421001China School of Mathematics and Statistics Henan University of Science and TechnologyLuoyang 471023China

The competition and cooperation among enterprises has become a hot topic and focus issue in today’s world. How to manage the enterprise well so as to achieve the maximum output is an important problem for enterprise managers. Optimizing output of two enterprises plays a key role in operating enterprises. Many scholars pay much attention to this aspect. However, the reports on the stability and Hopf bifurcation for fractional-order delayed competition and cooperation model of two enterprises are very few. This paper is concerned with the stability, the existence of Hopf bifurcation and the bifurcation control issue of fractionalorder delayed competition and cooperation model of two enterprises. Firstly, some new sufficient conditions that guarantee the stability and the existence of Hopf bifurcation for fractional-order delayed competition and cooperation model of two enterprises are obtained by regarding the delay as bifurcation parameter. Then a suitable time delayed feedback controller is designed to control the Hopf bifurcation for involved model. The study shows that the delay and the fractional order have an important effect on the stability and Hopf bifurcation of involved model. Some simulations justifying the validity of the derived analytical results are given. At last, we end this paper with a concise conclusion. The obtained results of this article are innovative and are of great significance in handling the competition and cooperation among enterprises.

关键词： bifurcation control competition and cooperation model enterprise stability hopf bifurcation fractional order elay

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bifurcation control and chaos in a linear impulsive system

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Chinese Physics B 2009年第12期18卷 5235-5241页

作者：蒋贵荣胥布工杨启贵 School of Mathematical Sciences South China University of Technology School of Mathematics and Computing Science Guilin University of Electronic Technology College of Automation Science and Engineering South China University of Technology

bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto＇s definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.

关键词： periodic solution bifurcation control chaos controller

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Analysis of complex intermittency in Boost converter from a bifurcation control viewpoint

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Science in China(Series F) 2008年第12期51卷 2135-2149页

作者： ZHOU YuFei JIANG XueDong CHEN JunNing School of Electronic Science and Technology Anhui University Hefei 230039 China

Due to undesirable interference via unintended coupling paths, switching converters may exhibit complex intermittency, which appears as a form of bifurcation undergoing regular operation, subharmonics, and chaos orderly and repeatedly for a long period of time. Such intermittent operation, being an unwanted operating state, should normally be avoided in power converters. This paper expounds the mechanism and conditions for the emergence of intermittency in a common current-mode controlled Boost converter. It is found that interference at frequencies near the switching frequency or its rational multiples may induce intermittent operation. The strengths and frequencies of the interfering signals determine the type and period of intermittency. The problem is analyzed by transforming the time-bifurcation analysis to a conventional parameter-bifurcation analysis. Based on this transformation, intermittency can be investigated from the bifurcation control viewpoint. Furthermore, the critical circuit parameter conditions for the emergence of intermittency can be predicted and compared with those from circuit simulation.

关键词： power converter intermittency bifurcation bifurcation control

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Hopf bifurcation Analysis and control of a New Lorenz-like System

Hopf Bifurcation Analysis and Control of a New Lorenz-like S...

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第26届中国控制与决策会议

作者： Zhang Zhonghua College of Science Northeast Dianli University

ISBN: (纸本)9781479937066

this paper is concerned with Hopf bifurcation behavior and bifurcation control of a new Lorenz-like ***,Hopf bifurcation type is studied based on the bifurcation stability norm,furthermore bifurcation period and characteristic exponent of system are *** the linear controller and the non-linear controller are applied to control the Hopf bifurcation of original system *** linear control,the Routh-Hurwitz criterion is adopted to give parameter conditions making Hopf bifurcation dissapear;For non-linear control,the Hopf bifurcation Normal Form of controlled system is obtained by using the direct Normal Form method,besides,according to coefficient of Normal Form,the impact of selection criteria of non-linear parameter on amplitude of limit cycle and Hopf bifurcation type are discussed,discussions show that when the non-linear parameter satisfies certain condition,bifurcation type of original system will be changed,and the periodic solution amplitude will be changed with the ***,theoretical results are verified by numerical simulations.

关键词： Lorenz-like system Hopf bifurcation bifurcation control Normal Form

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Hopf bifurcation Analysis and control for Electrical System of Military Vehicle

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Defence Technology（防务技术） 2009年第4期5卷 246-250页

作者：王宝华杨成梧 School of Power Engineering Nanjing University of Science and Technology

Electrical system of military vehicle is a typical parameterized nonlinear system where complicated bifurcations may exist and threaten its safe and stable operation. An algebraic criterion for Hopf bifurcation is presented briefly and applied to find Hopf bifurcation point of the electrical system with automatic voltage regulator(AVR) dynamics in military vehicle. Hopf bifurcation controllers are designed for this electrical system by using wash-out filter,linear feedback,nonlinear feedback and their combination. The linear feedback control makes the system bring Hopf bifurcation at preferable parameter,the nonlinear feedback control modifies the type of the bifurcation,and the wash-out filter enhances the system damping,thus,the Hopf bifurcation is eliminated and the electrical system stability is ensured. Simulation results show the controller's validity.

关键词： automatic control technology electrical system of military vehicles Hopf bifurcation bifurcation control stability

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ROBUST control OF PERIODIC bifurcation SOLUTIONS

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Applied Mathematics and Mechanics(English Edition) 2004年第3期25卷 263-271页

作者：梁建术陈予恕梁以德 Department of Mechanics Tianjin University Department of Building and Construction City University of Hong Kong

The topological bifurcation diagrams and the coefficients of bifurcation equation were obtained by C_L *** to obtained bifurcation diagrams and combining control theory,the method of robust control of periodic bifurcation was presented,which differs from generic methods of bifurcation *** can make the existing motion pattern into the goal motion *** the method does not make strict requirement about parametric values of the controller,it is convenient to design and make *** simulations verify validity of the method.

关键词： bifurcation topological structure bifurcation control C-L method

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Hybrid control of Delay Induced Hopf bifurcation of Dynamical Small-World Network

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Journal of Shanghai Jiaotong university(Science) 2017年第2期22卷 206-215页

作者：丁大为张肖芸王年梁栋 Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Electronics and Information Engineering Anhui University

In this paper, we focus on the Hopf bifurcation control of a small-world network model with *** emphasis on the relationship between the Hopf bifurcation and the time-delay, we investigate the effect of time-delay by choosing it as the bifurcation parameter. By using tools from control and bifurcation theory, it is proved that there exists a critical value of time-delay for the stability of the model. When the time-delay passes through the critical value, the model loses its stability and a Hopf bifurcation occurs. To enhance the stability of the model, we propose an improved hybrid control strategy in which state feedback and parameter perturbation are used. Through linear stability analysis, we show that by adjusting the control parameter properly, the onset of Hopf bifurcation of the controlled model can be delayed or eliminated without changing the equilibrium point of the model. Finally, numerical simulations are given to verify the theoretical analysis.

关键词： Hopf bifurcation hybrid control small-world network bifurcation control

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bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control

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Science China(Information Sciences) 2012年第1期55卷 200-213页

作者： CHEN PengNian1,QIN HuaShu2,WANG Yong3&HONG YiGuang2 1Department of Mathematics,China Jiliang University,Hangzhou 310018,China 2Institute of Systems Science,The Chinese Academy of Sciences,Beijing 100080,China 3Department of Mechanics,Peking University,Beijing 100871,China Department of Mathematics China Jiliang University Institute of Systems Science The Chinese Academy of Sciences Department of Mechanics Peking University

The paper deals with the problem of stabilization of stationary bifurcation solutions of nonlinear systems via dynamic output *** is emphasized that the parameter of the system is not directly *** introduce the concepts of uniform observability of the inverse of a function of state and input and N-order-input-to-state bifurcation *** on the concepts,we propose a new method for designing dynamic compensators that guarantee bifurcation stability for the closed-loop *** an example,we apply the general theory to active control of rotating stall in axial flow compressors by designing a stabilizing dynamic compensator for the three-state Moore-Greitzer model with a class of cubic compressor characteristics.

关键词： bifurcation control uniform observability dynamic output feedback rotating stall

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