A uniform semiglobal exponential stability (USGES) proof for a time-varying vector field guidance law used for path-following control of vehicles is presented. A sliding mode control is introduced for heading autopilot design and Lyapunov methods are used to derive the control law. The equilibrium point of the autopilot error dynamics is proven to be globally exponentially stable (GES). The main result is a time-varying vector field guidance law in cascade with the autopilot. A theorem ensures that the equilibrium point of the cascaded system is uniformly semiglobally exponentially stable. Both straight-line and curved-path path following scenarios are considered in the presence of ocean currents. Simulation studies are carried out to verify the theoretical results. The time-varying guidance laws can also be applied to vehicles in general such as aircraft, underwater vehicles, drones and autonomous vehicles.

提出了用于车辆路径跟踪控制的时变矢量场制导律的统一半全局指数稳定性（USGES）证明。引入滑模控制用于航向自动驾驶仪设计，并使用Lyapunov方法推导控制律。自动驾驶仪误差动力学的平衡点被证明是全局指数稳定的（GES）。主要结果是与自动驾驶仪级联的时变矢量场制导律。一个定理可确保级联系统的平衡点是一致的半全局指数稳定的。在存在洋流的情况下，都考虑了直线路径和弯曲路径路径。进行了仿真研究以验证理论结果。