Vector Liapunov Function Approach to Longitudinal Control of Vehicles in a Platoon

Abstract

An important aspect of an automated highway system design is the synthesis of an automated vehicle following system. Associated with automated vehicle following system is the problem of the stability of a string of vehicle, i.e., the problem of spacing error propagation, and in some cases, amplification upstream from one vehicle to another, due to some disturbance at the head of the string. In this paper, the novel method to determine the stability of a string of vehicle is established based on the vector Liapunov method. Based on the new results for the stability of string of vehicle, the controller is constructed by sliding mode control method. The stability domain of the controller parameters of the string of vehicles is enlarged.

String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

“…In particular, cases for p = 1 and p = 2, it is called exponentially mean and mean-square string stable. Zhang et al (2004) established a method to obtain the sufficient conditions of asymptotic string stability for deterministic interconnected systems with strong nonlinear coupling items. Firstly, using a similar method of the box theory, a lemma shall be proved in this section.…”

“…While taking into consideration the strong coupling interconnected systems, the above mentioned methods have some obvious limitations. Zhang, Suda, Iwasa, and Komine (2004) nonlinear interconnected systems with strong coupling items by means of the vector Lyapunov function method and established the box theory, a new way for the designing of nonlinear control systems, which obtained sufficient conditions of asymptotic string stability and was easy to deal with the infinite-dimension nonlinear interconnected systems with strong coupling items.…”

“…The literatures (Chu 1974;Socha and Popp 1986;Swaroop et al 1994;Swaroop and Hedrick 1996;Mao 1996;Zhang et al 2004) only studied the deterministic interconnected systems and ignored the random factors, but stochastic uncertainty does exist in many situations such as the vehicle-running environment, the vehicle system modelling, the acquisition and transmission of vehicle and road signal and so on. The controller is designed based on the system stability, so it is necessary to study the stability of infinite-dimension stochastic interconnected systems.…”

“…In this paper, a lemma is derived by using the similar idea of the paper (Zhang et al 2004) and sufficient conditions for the stability of a class of infinite-dimensional stochastic interconnected large-scale systems with variable delays are established. A criterion for exponential string stability of the systems is obtained.…”

Variable structure adaptive control for vehicle longitudinal following in a platoon

“…Due to the vector Lyapunov function method is efficient tool in the stability analysis of nonlinear large-scale systems [13], In Ref. [16], vector Lyapunov function method is applied in the stability analysis of vehicles string, the new string stability conditions are obtained and the stability domain of control parameters is larger than that in [12]. Because realistic vehicle following designs must also address parametric uncertainties such as mass of the vehicle, aerodynamic drag, and tire drag, However, in [16], the effect of parametric uncertainty on the platoon performance was neglected.…”