Adaptive Fixed-Time Control of High-Order Fully Actuated Systems Using Dynamic Regressor Extension and Mixing Estimators

This paper investigates the adaptive fixed-time control problem of the high-order fully actuated (HOFA) systems with parametric uncertainties. Using the recently introduced dynamic regressor extension and mixing parameter estimation technique, we propose a novel fixed-time parameter estimator that offers two distinctive advantages: 1) the convergence rate of each parameter error can be tuned in an independent way. 2) the estimates of the unknown parameters converge to the true values in fixed-time under the weak interval excitation condition. Building upon this estimator, we further develop an adaptive controller that ensures fixed-time tracking control of uncertain HOFA systems. The effectiveness of the proposed control scheme is rigorously verified through numerical simulations of robotic manipulator systems.