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Bifurcation analysis and control study of improved full-speed differential model in connected vehicle environment |
| Wen-Huan Ai(艾文欢)1,†, Zheng-Qing Lei(雷正清)1, Dan-Yang Li(李丹洋)1, Dong-Liang Fang(方栋梁)1, and Da-Wei Liu(刘大为)2 |
1 College of Computer Science and Engineering, Northwest Normal University, Lanzhou 730070, China;
2 College of Electrical Engineering, Lanzhou Institute of Technology, Lanzhou 730050, China |
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Abstract 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.
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Received: 17 November 2023
Revised: 14 March 2024
Accepted manuscript online: 07 April 2024
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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47.52.+j
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(Chaos in fluid dynamics)
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45.70.Vn
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(Granular models of complex systems; traffic flow)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 72361031) and the Gansu Province University Youth Doctoral Support Project (Grant No. 2023QB-049). |
Corresponding Authors:
Wen-Huan Ai
E-mail: wenhuan618@163.com
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Cite this article:
Wen-Huan Ai(艾文欢), Zheng-Qing Lei(雷正清), Dan-Yang Li(李丹洋), Dong-Liang Fang(方栋梁), and Da-Wei Liu(刘大为) Bifurcation analysis and control study of improved full-speed differential model in connected vehicle environment 2024 Chin. Phys. B 33 070503
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