The longitudinal control for a platoon of connected and automated vehicles is a popular topic in transportation engineering, nowadays. However, a majority of existing results about the cooperative/distributed platoon control are based on linear models that are derived from nonlinear vehicular dynamics by exact feedback linearization. This nonlinear–linear transformation asks for a complete priori knowledge of vehicular dynamics, which could be difficult to obtain in practice. To overcome this disadvantage and address multiuncertainties including both unknown plant parameters and unknown control coefficients in third-order vehicular node dynamics, this paper proposes a distributed backstepping control scheme in a networked environment. Unknown parameters are identified online, and both internal stability and string stability for constant distance spacing policy are established. Simulation studies are carried out by comparing the adaptive control proposed in this paper with the robust control in the state-of-the-art algorithms.

The longitudinal control of the platoon of connected and automated vehicles (CAVs) has gained extensive attention in recent transportation research. A majority of existing results are based on linearized third-order vehicular models, under the premise that a complete priori knowledge of vehicle dynamics is available. This article focuses on a general class of third-order nonlinear CAVs with parametric uncertainty and unknown external disturbance which cannot be linearized. A vehicle-to-vehicle (V2V) communication-based cooperative adaptive backstepping control scheme is proposed, in which unknown parameters and disturbance bounds are estimated on-line. Since the transfer function of linear systems cannot be applied to nonlinear systems to guarantee string stability, asymmetric time-varying constraints are employed to prevent the spacing errors from growing up. A realistic example is considered to verify the feasibility of the control algorithm.

This article proposes a constructive method for sampled-data extremum seeking (ES) with square wave dithers and constant delays, by using two time-delay approaches: one to averaging and the other to sampled-data control. We consider gradient-based ES for static maps which are of quadratic forms. By transforming the ES system to the time-delay system, we have developed a stability analysis via a Lyapunov–Krasovskii method. We derive the practical stability conditions in terms of linear matrix inequalities for the resulting time-delay system. The time-delay approach offers a quantitative calculation on the upper bound of the dither and sampling periods, constant delays that the ES system is able to tolerate, as well as the ultimate bound of the extremum seeking error. This is in the presence of uncertainties of extremum value and extremum point.

While the existing literature on delay-adaptive control concentrates on uncertain plants with discrete input delays, this article proposes a predictor feedback for stabilization of uncertain linear systems with distributed input delays. A finite-dimensional linear system with distributed actuator delay may come with five types of uncertainties: unknown delay, unknown delay kernel, unknown plant parameters, unmeasurable finite-dimensional plant state, and unmeasurable infinite-dimensional actuator state. For different combinations of uncertainties, distinct control designs are developed in the article, from which the users can make selections to address a vast range of problems they face.

This paper proposes a decentralized predictor based feedback to compensate large delays in large-scale interconnected systems. The full-state of each subsystem is assumed to be unmeasurable and the observer-based output feedback is employed. Two methods are used to tackle the large delays: the backstepping-based partial differential equation (PDE) approach and the reduction-based ordinary differential equation (ODE) approach. The PDE method is used for continuous-time control and manages with larger delays, whereas the ODE method is applicable to sampled-data implementation under discrete-time measurement, as well as to delayed interconnections.