Adaptive global stabilization of chained-form systems with multiple disturbance and strong nonlinear drifts

This article investigates the stabilization of chained-form nonholonomic systems with strong drifts, multidisturbances, and unknown constant parameters. The disturbances include the matched disturbance with bounded variation and the unknown time-varying unmatched disturbance. A nonlinear disturbance observer is skillfully constructed to evaluate the matched disturbance and a disturbance estimation is used in the virtual controls to compensate the unmatched disturbance. By using a new input-to-state scaling scheme, the original nonholonomic system is transformed into a strict feedback form. Combining back-stepping technique with disturbance observer-based control (DOBC), a composite DOBC and global adaptive stabilization controller is proposed. A switching strategy based on control input magnitude instead of time is proposed to avoid uncontrollability. By using Lyapunov tools, all the states in the system are proved to be uniformly ultimate bounded. Simulations demonstrate the effectiveness of the proposed strategies.