Dynamical analysis of an optimal velocity model with time-delayed feedback control

• Published in: Communications in nonlinear science & numerical simulation Vol. 90; p. 105333
• Main Authors: Jin, Yanfei, Meng, Jingwei
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2020; Elsevier Science Ltd
• Subjects: An optimal velocity model; Closed loop systems; Control stability; Control systems; Definite integral stability method; Eigenvalues; Eigenvectors; Feedback control; Feedback control systems; First stable interval; Flow stability; Hopf bifurcation; Intervals; Mathematical models; Multivariable control systems; Numerical analysis; Systems stability; Time delay; Time lag; Traffic congestion; Traffic control; Traffic flow; Traffic jams; Velocity; First stable interval; Time delay; Definite integral stability method; An optimal velocity model
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2020.105333

•The stability and bifurcation are analyzed in an OVM with time-delayed feedback control of velocity differences.•The first stable intervals of time delay and feedback gain are determined by using the improved definite integral stability method.•The control method can suppress traffic jam by choosing feedback gain and time delay from the first stable intervals.•The proposed method provides an effective and simple way to design controller. In this paper, the dynamical behaviors of an optimal velocity model (OVM) with delayed feedback control of velocity difference is studied. By analyzing the transcendental characteristic equation, the stable region of controlled OVM is obtained and the critical condition for Hopf bifurcation is derived. To stabilize the unstable traffic flow and control the bifurcations, the definite integral stability method can be applied to determine the first stable intervals of time delay and feedback gain by calculating the number of all unstable eigenvalues of the characteristic equation. That is, when the time delay and the feedback gain are chosen from the corresponding stable intervals, the controlled OVM is stable and the stop-and-go traffic waves disappear. The numerical simulations in the case studies indicate that the proposed control strategy can suppress the traffic jams effectively and enhance the stability of traffic flow significantly.