Adaptive λ-tracking for higher relative degree systems

This paper proposes a relatively simple adaptive controller for systems with higher relative degree. Only little information on the system is needed: only 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 achieves λ-tracking for a large class of nonlinear systems and 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. The controller’s adaptation converges and the control objective is achieved at least asymptotically.