Delay margin comparison in a velocity-only versus headway-only connected vehicle model

Two different connected vehicle models are considered: one based on only using velocity measurements and the other using only headway, where each model is affected by delays due to human reaction times and sensing and communication lines. The presence of delays is established between any two vehicles that are neighbors as determined by the underlying network topology. The main focus here is to put light into our understanding of how much of time delay can the equilibrium of these models tolerate before becoming unstable. To this end, we compute, using the parallel processing computational tool Delay Margin Finder (parDMF), the delay margin of the equilibrium dynamics and discuss design trade-offs. We report that delay margin in the headway-only model is much less sensitive against the presence/absence of links in the network and that this model can have larger delay margin when larger number of vehicles are capable of communicating with other vehicles in the platoon.

Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality

In this paper, the delay-dependent stability of haptic systems is studied by developing a new stability criterion. Firstly, the haptic system inevitably introduces time delays by using communication networks to transmit information between the controller and the haptic device. When discussing the stability of the haptic system near its operating point, the original nonlinear system is modeled as a linear system with the time delay mentioned above. In addition, a suitable augmented Lyapunov–Krasovskii functional (LKF) with more integral forms is constructed and an auxiliary function-based integral inequality is applied to estimate the derivative of the proposed LKF. Then, a less conservative delay-dependent criterion in terms of the linear matrix inequality (LMI) is derived to calculate the delay margin for the haptic system. Finally, case studies are carried out based on a one degree of freedom haptic system. The results show that, compared with criteria in existing works, the proposed criterion can obtain more accurate results and require less calculation complexity, and, with the increase in virtual damping in a certain range, the stable upper bound of the haptic system increases at first and then decreases.