Modelling and Prediction of Random Delays in NCSs Using Double-Chain HMMs

This paper is concerned with the modelling and prediction of random delays in networked control systems. The stochastic distribution of the random delay in the current sampling period is assumed to be affected by the network state in the current sampling period as well as the random delay in the previous sampling period. Based on this assumption, the double-chain hidden Markov model (DCHMM) is proposed in this paper to model the delays. There are two Markov chains in this model. One is the hidden Markov chain which consists of the network states and the other is the observable Markov chain which consists of the delays. Moreover, the delays are also affected by the hidden network states, which constructs the DCHMM-based delay model. The initialization and optimization problems of the model parameters are solved by using the segmental K-mean clustering algorithm and the expectation maximization algorithm, respectively. Based on the model, the prediction of the controller-to-actuator (CA) delay in the current sampling period is obtained. The prediction can be used to design a controller to compensate the CA delay in the future research. Some comparative experiments are carried out to demonstrate the effectiveness and superiority of the proposed method.