Modeling and estimation of networked control systems with time delays based on CTHMM

Network-induced delays in a networked control system (NCS) are stochastic continuous variables that depend on the current network state, which, as an abstract and hidden variable, can not be well defined but can be perceived by the observation of the packet-delay process. We model the network in an NCS as a hidden Markov chain and the network delay as stochastic variable whose probability density function depends on the Markov chain state (i.e. network state). Thus, the network state estimation is a continuous-time hidden Markov model (CTHMM) estimation problem. To derive the CTHMM of the NCS under study, we propose the Expectation Maximization (EM) algorithm to learn the parameters of the CTHMM based on the packet delay observations. The derived CTHMM make it possible in the future for us to predict the next network state and then choose a proper one from several control laws, which have been designed in advance to guarantee the performance of the NCS.