Robust Adaptive Control for a Class High-order Cascaded Uncertain Nonlinear Systems

The paper studies the problem of robust adaptive control for a class of high-order cascaded nonlinear systems in presence of unmodeled dynamics, nonlinear uncertainties and parameter uncertainties. The system is different from usually feedback linearizable systems: it consists of a series of chains of power integrators perturbed by a low-triangular vector field and its control input is not linear. Under triangular bound conditions, applying Lyapunov second method and tuning function adaptive backstepping theory, a smooth state feedback controller is explicitly constructed, which renders all states of closed-loop systems be global uniform ultimate boundness, and the output converge to a small neighborhood of the origin for all admissible uncertainties. Eventually a numerical example is given to illustrate the validity of the conclusion.