Nonlinear Discrete-time System Identification without Persistence of Excitation: Finite-time Concurrent Learning Methods

Abstract

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 finitetime 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.

Fixed-time Stability of Discrete-time Autonomous Systems

“…Finite-time stability [1] has been extensively studied for the finitetime control of discrete-time (DT) systems [2]- [4] and continuoustime (CT) systems [5]- [7], as well as finite-time identification [8]- [16]. In the finite-time stability, however, the settling (i.e., convergence) time, depends on the system's initial condition, and, thus, cannot be specified a priori.…”

“…While most real-world systems are CT in nature, DT systems are of great importance since systems are typically discretized and controlled with digital computers and micro-controllers in real-world applications. Even though finite-time stability of DT is studied in [15], [16], [35], [36], fixed-time stability of DT systems is surprisingly unsettled, despite its practical importance. This gap motivates us to present fixed-time Lyapunov stability conditions that pave the way for realization of fixed-time control and identification of DT systems through designing appropriate controllers and adaptation laws, respectively.…”