Impact of delayed acceleration feedback on the classical car-following model. (17th July 2020)

• Record Type: Journal Article
• Authors: Kamath, Gopal Krishna; Jagannathan, Krishna; Raina, Gaurav
• Is Part Of: IMA journal of applied mathematics. Volume 85:Number 4(2020)
• Page Start: 584
• Page End: 604
• Publication Date: 2020-07-17
• Subjects: transportation networks -- car-following models -- delayed acceleration feedback -- stability -- Hopf bifurcation -- convergence -- string stability -- robust stability; Mathematics -- Periodicals; Mathematics; Periodicals; 519
• DOI: 10.1093/imamat/hxaa019
• Languages: English
• ISSNs: 0272-4960

Abstract

Abstract: Delayed acceleration feedback (DAF) is known to have a positive impact on the stability properties of dynamical models in several applications. Motivated by this, we study the impact of DAF on the classical car-following model (CCFM). First, we show that DAF shrinks the locally stable region. We then show that the resulting model, similar to the CCFM, loses local stability via a Hopf bifurcation. However, DAF decreases the amplitude and increases the frequency of the resulting limit cycles. Additionally, we show that DAF is detrimental to the CCFM due to $(i)$ destruction of the non-oscillatory property of its solutions, $(ii)$ increased risk of string instability and $(iii)$ reduced resilience towards parametric uncertainty. Thus, we report a relevant application wherein DAF degrades the performance across several metrics of practical interest. Thus, our work motivates a systematic study of controllers that can guarantee performance enhancement. We complement our analytical results with stability charts and a bifurcation diagram.