Robust direct adaptive control of nonlinear uncertain systems with unknown disturbances

This paper addresses a direct adaptive control approach to the problems of adaptive stabilization of a class of multivariable nonlinear systems affected by time-varying uniformly bounded affine perturbations, which are confined to a characterized class. The proposed framework is Lyapunov-based, and the nominal control has augmented with a robustifying component, guaranteed asymptotic stability of the closed-loop systems. Furthermore, the framework can also extended to solve the problems with exogenous disturbances, uncertain nonlinearities and unmodeled dynamics. As applications of our results we address the problems of control of chaotic oscillator, and the tracking control of one-link rigid robot under gravitation field and flexible joint robot.