This paper presents a novel observer-based gain-scheduling path following control algorithm for autonomous electric vehicles subject to time delay. Firstly, the lateral dynamic model of the autonomous electric vehicle is constructed by a polytope with four vertices, in which the issues of the time-varying longitudinal velocity and nonlinear tyre dynamics are accurately described. Secondly, taking the time delay encountered in the process of signal transmission into consideration, the observer-based path following controller is proposed by using easily measured vehicle states. In the algorithm, the observer and controller gains are gain scheduled according to the actual longitudinal velocity. Thirdly, based on Lyapunov stability theory, an appropriate Lyapunov–Krasovskii functional is constructed to derive sufficient conditions of the controller, which is effective to ensure the asymptotical stability of the closed-loop path following error system with a guaranteed $H_{\mathrm{\infty }}$ performance. Specially, for ease of computation, the sufficient conditions of controller design are developed in terms of a set of linear matrix inequalities. Finally, numerical simulations are implemented to illustrate the efficiency and superiority of the proposed method in comparison with the existing method.

本文提出了一种新颖的基于观测器的增益调度路径跟踪控制算法，用于受时延影响的自主电动汽车。首先，由一个具有四个顶点的多面体构建自动驾驶电动汽车的横向动力学模型，其中准确描述了时变纵向速度和非线性轮胎动力学问题。其次，考虑到信号传输过程中遇到的时间延迟，利用容易测量的车辆状态，提出了基于观测器的路径跟随控制器。在该算法中，观测器和控制器的增益是根据实际纵向速度进行增益调度的。第三，基于Lyapunov稳定性理论，构造合适的Lyapunov-Krasovskii泛函，推导出控制器的充分条件，$H_{\mathrm{\infty }}$表现。特别地，为了便于计算，控制器设计的充分条件是根据一组线性矩阵不等式来开发的。最后，通过数值模拟来说明所提方法与现有方法相比的效率和优越性。