Adaptive Non-linear Tracking with Complete Compensation of Unknown Disturbances

We consider a class of single-input, single-output non-linear systems which are transformable into the parametric-strict-feedback canonical form with unknown constant parameters. A state-feedback adaptive controller is proposed which achieves global asymptotic tracking of the reference signal with simultaneous complete compensation of bounded disturbances generated by a linear exosystem of the known order but with unknown parameters. The main contribution of the paper consists of a new parameter-dependent non-linear observer for unknown and inaccessible deterministic disturbances. The proposed control law contains a regulating component designed via the adaptive integrator backstepping technique and the compensating component providing adaptive counteracting of unknown external disturbances and global stabilisation of the closed-loop system.