Adaptive backstepping-like control of discrete-time high-order strict-feedback systems with asymptotic parameter estimations

This paper proposes an adaptive backstepping-like control approach with asymptotic parameter estimations for a class of discrete-time high-order strict-feedback nonlinear systems (SFNSs). By constructing a set of discrete-time low-pass filters and auxiliary variables, the parameter estimation errors are reconstructed. Based on the reconstruction results, an adaptive backstepping-like control algorithm is designed. It is proved by using the Lyapunov theory that the system output and the parameter estimation errors could converge to zero. The proposed discrete-time adaptive control method is finally applied to the control of a single-link manipulator, and the simulation results show the effectiveness of the design result.