An extended AUDI algorithm for simultaneous identification of forward and backward paths in closed-loop systems

In closed-loop system identification, most of the existing methods only focus on the forward path, yet few on simultaneous identification of the forward and backward paths. Meanwhile, an augmented UD identification (AUDI) algorithm has been proved effective in open-loop system identification, but it only extracts the forward path information, while not including the backward path information provided in an augmented information matrix, which is helpful for the closed-loop system identification. In this paper, an extended AUDI (EAUDI) is proposed to simultaneously identify the model orders and parameters of both forward and backward paths of a closed-loop system. The conditions of identifiability and uniform convergence for closed-loop systems using the EAUDI algorithm are also given. The effectiveness of this algorithm is demonstrated by a numerical example.