Adaptive robust control of a class of nonlinear systems with unknown control coefficient and disturbances

Incorporating Nussbaum function gain into adaptive backstepping, this paper develops an adaptive nonlinear robust control scheme for a class of nonlinear strict-feedback systems with completely unknown control coefficient and unknown bounded disturbance. The proposed design method does not require any a priori knowledge of the signs of the unknown control coefficient. A leakage term based on σ-modification is adopted to prevent the parameter drifts in the adaptive law. By means of Lyapunov function and related lemmas, it is proved that the designed adaptive robust nonlinear controller can guarantee the stability and the global uniform ultimate boundedness of all signals of the resulting closed-loop system. The prescribed control performances of the system can be guaranteed by an appropriate choice of the design parameters. Simulation studies illustrate the feasibility and effectiveness of the presented approach.