Adaptive backstepping for trajectory tracking of nonlinearly parameterized class of nonlinear systems

Adaptive control is of interest in control systems design not only for its capability to improve performance and reliability but also for handling parameters uncertainties, external disturbances and modeling inaccuracies. This paper addresses a systematic procedure design to develop an adaptive backstepping tracking control approach for a second-order class of single input-single output (SISO) nonlinear systems where the controllability condition is checked. The considered class covers general feedback linearizable and nonlinearly parameterized systems. Both of the control and adaptation laws are synthesized simultaneously based on the positivity and Lyapunov design approaches. Simulation results for an illustrative numerical example are provided to illustrate in this case the effectiveness of the proposed controller.