Nonlinear Discrete-time Systems' Identification without Persistence of Excitation: A Finite-time Concurrent Learning

This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. A finite-time concurrent learning approach is presented to approximate the uncertainties of the discrete-time nonlinear systems in an on-line fashion by employing current data along with recorded experienced data satisfying an easy-to-check rank condition on the richness of the recorded data which is less restrictive in comparison with persistence of excitation condition. Rigorous proofs guarantee the finite-time convergence of the estimated parameters to their optimal values based on a discrete-time Lyapunov analysis. Compared with the existing work in the literature, simulation results illustrate that the proposed method can timely and precisely approximate the uncertainties.