Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems

The authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems which are described in the parametric strict-feedback form and are subject to additional exogenous disturbance inputs. Their approach to adaptive control is performance-based, where the objective for the controller design is not only to find an adaptive controller, but also to construct an appropriate cost functional, compatible with desired asymptotic tracking and disturbance attenuation specifications, with respect to which the adaptive controller is "worst case optimal". Three main issues of the paper are: the backstepping methodology, worst case identification schemes, and singular perturbations analysis. Closed-form expressions have been obtained for an adaptive controller and the corresponding value function. A numerical example involving a third-order system is given.