Adaptive RISE-based tracking control of uncertain nonlinear systems: A FAS approach

A fully actuated system (FAS) approach integrated with adaptive robust integral of the sign of the error (ARISE) feedback control strategy is proposed for multi-input multi-output nonlinear systems in the presence of both external disturbances and parametric uncertainties. Owing to an inability to eliminate unmeasured disturbances and model inaccuracies simultaneously, the existing results based on the FAS approaches are typically limited to the uniformly ultimate boundedness of the tracking errors. To achieve the asymptotic tracking performance confronted with parametric uncertainties and time-varying disturbances, an ARISE feedback controller with desired compensation is synthesized to suppress the adverse effects arising from nonlinearity and uncertainty of the system. The improvements compared to the traditional RISE feedback control are attributed to two aspects: (i) the feedback gains in the RISE term are adjustable-online without having to know the prior bounds of disturbances and their time derivatives; (ii) a desired compensation-based adaptive feedforward term, primarily employing the desired trajectories in place of the measured states, could weaken the underlying interaction between the adaptive compensation and robustness part. A rigorous stability analysis is provided to demonstrate that the system state can asymptotically track a bounded desired trajectory in spite of bounded disturbances and parametric uncertainties. Comparative simulations on an under-actuated planar manipulator, possessing an equivalent multi-order FAS model, have been conducted to verify the effectiveness and merits of the developed controller. Experimental validation on a two-wheeled self-balancing robot is also provided to show the feasibility of the proposed approach.