Immersion and invariance based composite adaptive control of nonlinear high-order systems

A new nonlinear composite adaptive control based on immersion and invariance theory is presented for a class of high-order system with parametric uncertainty. The main feature of this control scheme lies in the construction of the adaptive law, which is driven by both tracking error and prediction error. The tracking-error based adaptation law is first constructed using immersion and invariance theory, then the prediction-error based adaptation law is added to it, thus makes a composite adaptive control law. The combination is applied to the immersion and invariance based adaptive control with improved performance. Stability analysis is presented using Lyapunov theory, which shows asymptotical convergence of the tracking error to zero. The validity of the proposed control scheme is illustrated through numerical simulations.