Initialization of the HMM-based delay model in networked control systems

When hidden Markov models (HMMs, including discrete HMM and semi-continuous HMM) are used to model and predict the random delays in networked control systems, there are five parameters needed to be estimated. They are the number of different network states, the initial distribution of the network states, the state transition matrix of the hidden Markov chain formed by the network states, the number of different delay observations in the discrete HMM (DHMM) or the number of the Gaussian densities in the semi-continuous HMM (SCHMM), and the delay observation matrix in the DHMM or the combination of the mixture Gaussian distributions in the SCHMM. How to initialize these parameters is very crucial to the precision of the modeling and prediction of random delays. In this paper, the entropy and cluster based initialization methods are proposed to obtain the optimal initialization of these parameters. The effectiveness of the proposed methods is demonstrated by some simulation examples.