Nonlinear Discrete-time System Identification without Persistence of Excitation: Finite-time Concurrent Learning Methods
This addresses the challenge of system identification in control and robotics by reducing restrictive excitation conditions, though it appears incremental as it builds on existing concurrent learning methods.
The paper tackles the problem of finite-time learning for unknown discrete-time nonlinear systems without requiring persistence of excitation, presenting two concurrent learning methods that achieve finite-time convergence of estimated parameters to optimal values, with simulation results showing timely and precise approximation of uncertainties.
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. Two finite-time concurrent learning methods are presented to approximate the uncertainties of the discrete-time nonlinear systems in an online 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. For the proposed finite-time concurrent learning methods, rigorous proofs guarantee the finite-time convergence of the estimated parameters to their optimal values based on the discrete-time Lyapunov analysis. Compared with the existing work in the literature, simulation results illustrate that the proposed methods can timely and precisely approximate the uncertainties.