Parameter estimation for a class of time‐varying systems with the invariant matrix

Abstract

This article is concerned with the identification of time-varying systems. Differently from the conventional polynomial approximation approaches, the changing laws of the time-varying parameters are considered to build the identification model for the time-varying systems. Specifically, the concept of the invariant matrix is put forward to characterize the time-varying parameters and to establish the state-space model with regard to the system parameters. Then this article proposes a stacked state estimation algorithm to achieve the time-varying parameter estimation. Moreover, for the purpose of enhancing the computational efficiency, a detached state estimation algorithm is proposed by reducing the dimension of the state vector to reconstruct the state equation. Finally, a numerical simulation example is employed to demonstrate the effectiveness of the proposed algorithms.

Hierarchical recursive gradient identification of Hammerstein nonlinear systems based on the key term separation

“…According to Equations (7), one combines the linear partial parameter vectors a and b. Then model ( 8) can be equivalently expressed as…”

“…Therefore, the foremost challenge is to overcome the hurdle of system modeling. System identification techniques that rely on measured data provide an efficient approach to establishing a mathematical model of the system [4,5,6,7]. The estimation of system parameters is a crucial prerequisite for effective system identification and thus has been the subject of extensive scrutiny in the field of control engineering.…”

Hierarchical estimation methods based on the penalty term for controlled autoregressive systems with colored noises

“…Identification methods can be derived through solving an optimization problem such as minimizing some criterion functions about the squared sum of the differences between the system outputs and the model outputs. Recently, many identification methods have been proposed for linear systems, 12 time-varying system, 13 bilinear systems 14 and nonlinear systems. [15][16][17] The objective function of machine learning algorithms is empirical risk plus structural risk.…”