Recursive Identification Algorithms for a Class of Linear Closed-loop Systems

This paper focuses on the identification problems for a class of linear closed-loop systems. On one hand, the identifiability condition is investigated for the case where the controller is in series with the plant on the forward channel. On the other hand, the identification model is derived after parametrization, in which the parameter vector only contains the parameters of the controlled plant instead of the whole closed-loop system, and a recursive least squares algorithm and a stochastic gradient algorithm are proposed for closed-loop systems. In order to improve the parameter estimation accuracy, a forgetting factor and a convergence index are introduced into the proposed stochastic gradient algorithm. The simulation results demonstrate the effectiveness of the proposed algorithms.