Adaptive stabilization for cascade nonlinear systems using the backstepping and control Lyapunov function techniques

Adaptive stability control can be made more applicable by incorporating it into the estimator of nonlinear time variant uncertainties. In order to achieve input-to-state stability (ISS) with respect to unknown bounded disturbances, the backstepping and control Lyapunov function (CLF) techniques were used to design an adaptive controller of full-state feedback for certain cascade nonlinear systems. It shows that update laws can estimate unknown bounded disturbances. This requires less information on the disturbance as a part of the stabilizing control law. This design method achieves the desired property: robust global asymptotical stability. The results of the illustrative example in the disturbed pendulum show that some advances are made in stabilizing cascade nonlinear system with the unknown disturbance.