Online identification of time‐delay jump Markov autoregressive exogenous systems with recursive expectation‐maximization algorithm

Abstract

Summary This article considers the identification problem of the jump Markov autoregressive exogenous (JMARX) systems with unknown invariant time‐delay under the framework of recursive expectation‐maximization (REM) algorithm. In this article, a recursive Q‐function is formulated for the JMARX systems, based on which the recursive sufficient statistics are obtained. Then, the parameter vectors, variance, transition probability matrix, and time‐delay are recursively estimated. A numerical example and a simulated continuous fermentation reactor process are employed to illustrate the effectiveness of the proposed algorithm.

Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator

“…To overcome this difficulty, inserting (12) into (15), (13) into (16), and (14) into (17), we have the following relations:…”

“…11 A deal of research has been conducted on the identification of linear systems, bilinear systems, 12,13 nonlinear systems 14,15 and time-delay systems. [16][17][18] However, the nonlinear terms in the bilinear model pose some challenges to bilinear system identification. During the past decades, the minimal order state observer and the stable state estimator were considered for bilinear systems, and their necessary conditions for the existence of observers were discussed, but the estimation error depended on the input of the systems.…”

“…A deal of research has been conducted on the identification of linear systems, bilinear systems, 12,13 nonlinear systems 14,15 and time‐delay systems 16‐18 . However, the nonlinear terms in the bilinear model pose some challenges to bilinear system identification.…”

Expectation‐maximization‐based infrared target tracking with time‐varying extinction coefficient identification

“…For the problem described in the previous section, the JIE scheme is derived by fully considering the coupling of the time‐varying parameters and the target state. As a systematical method to address the JIE problem, the EM iterate alternates between performing an expectation (E) step and a maximization (M) step 25‐35 . The analytical implementation of EM‐based JIE is as follows.…”

“…As a systematical method to address the JIE problem, the EM iterate alternates between performing an expectation (E) step and a maximization (M) step. [25][26][27][28][29][30][31][32][33][34][35] The analytical implementation of EM-based JIE is as follows.…”