Adaptive control of non-linearly parameterised pure-feedback systems

This study proposes an adaptive tracking control approach for non-linearly parameterised pure-feedback systems with completely non-affine property. Using the parameter separation technique, a state predictor is developed for deriving adaptive laws of non-linearly connected parameters. The proposed adaptive control system is designed by a combination of the backstepping and singular perturbation concept where the virtual controllers and the actual controller are defined as solutions of fast dynamic equations which accomplish the time-scale separation between the state predictor and controllers. The Lyapunov-based adaptive laws guarantee that the predictor states track the system states with bounded errors, and thus the tracking error between the system output and the desired signal is bounded. Finally, simulation results are provided to illustrate the effectiveness of the proposed control system.