Abstract
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.
Highlights
In traditional control systems, system nodes are usually connected by the port to port wiring, which may cause many problems such as the difficult wiring and maintenance and the low flexibility and reliability
At is to say, the current delay is governed by the current network state as well as the previous delay. erefore, the socalled double-chain hidden Markov model is introduced in this paper to model the random delays in networked control systems (NCSs). e contribution of this paper lies in the novel modelling method (i.e., DCHMM) that considers the relationship between the random delay and the network state as well as the relationship between the random delay and its previous value. is is the first time in the literature that both the network status and the delay itself are considered simultaneously in the delay modelling
Different from the existing modelling methods, this paper considers the dependency between the network states and the CA delays as well as the interdependence between the CA delays. e dependency between the network states and the CA delays is modelled as a hidden Markov model, and the interdependence between the CA delays is modelled as a Markov chain
Summary
System nodes (such as sensors, controllers, and actuators) are usually connected by the port to port wiring, which may cause many problems such as the difficult wiring and maintenance and the low flexibility and reliability. Under the Markov chain-based delay model, the NCS is often modelled as a Markovian jump linear system (MJLS), and many control methodologies (e.g., robust control, predictive control, and fuzzy control) can be used to analyze and synthesize the NCSs with random delays. In the HMM-based delay model, the stochastic distribution of current delay is only governed by the current network state. Erefore, the socalled double-chain hidden Markov model (denoted as DCHMM) is introduced in this paper to model the random delays in NCSs. e contribution of this paper lies in the novel modelling method (i.e., DCHMM) that considers the relationship between the random delay and the network state as well as the relationship between the random delay and its previous value.
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