Stratified Adaptive Finite-Time Tracking Control for Nonlinear Uncertain Generalized Vehicle Systems and Its Application

We present a stratified adaptive finite-time tracking control (SAFTTC) system, and apply the methodology to trajectory tracking of nonlinear uncertain generalized vehicles. The modeling approach separates vehicle pose dynamics and actuator dynamics into indirect and direct modes, respectively. To track the reference trajectory of the task, an adaptive finite-time virtual reference trajectory (AFTVRT) generator is designed to converge to a first switching surface. The output generated by the AFTVRT is a virtual reference that must then be tracked by the direct modes. Direct mode tracking of the AFTVRT output is achieved by a second, AFTTC, which is designed to converge to a second switching surface. Simple adaptive laws for AFTVRT and AFTTC learn the upper bounds of both the indirect mode and direct mode uncertainties, and convergence to both switching surfaces is with linear dynamics and fractional order of tracking errors. Stability of the closed-loop system is ensured by the Lyapunov stability theory. An application for tracking a pair of nested, interlocking circular trajectories by an omnidirectional autonomous ground vehicle also confirms effectiveness and robustness of the proposed adaptive control system. In the absence of adaptive learning, the system is unable to track the trajectory.