Adaptive λ-tracking for nonlinear higher relative degree systems

This paper proposes a relatively simple adaptive controller for nonlinear systems with higher relative degree. The controller achieves λ-tracking for a large class of nonlinear systems, i.e. it asymptotically stabilizes the system up to an error of at most λ which is chosen by the user. Only little information on the system is needed in the sense that no model needs to be known for the controller design, but only structural information like the relative degree and a lower bound on the positive high-frequency gain. The zero-dynamics does not need to be asymptotically stable, boundedness is sufficient. The controller consists of a high-gain observer, a high-gain observer-state feedback and a common adaptation of both high-gain parameters. The adaptation increases the gains of the observer and the state-feedback whenever the control objective, namely that the tracking error is of magnitude not larger than λ, is not attained. It is proved that the controller's adaptation converges and the control objective is achieved at least asymptotically.