Identification of time-delay Markov jumps autoregressive system with recursive expectation maximum and convex optimization algorithm

A novel proposed approach of the recursive expectation–maximization (REM)–convex optimization algorithm is developed to solve the parameter identification problem of the Markov jump autoregressive exogenous (MJARX) systems with unknown time delays. First, the REM algorithm is employed for identifying the unknown time delay of the system, based on which the time-delay sequence is obtained. Subsequently, the model parameter vector is determined by the convex optimization algorithm. Finally, the transition probability matrix and variance are calculated based on the minimized mean square error. A numerical example and simulated continuous fermentation reactor process are implemented to demonstrate the effectiveness of the proposed algorithm. The identification results are better than the expectation–maximization algorithm and REM algorithm results.