State estimation of Boolean control networks under stochastic disturbances with random delay in measurements

In the existing literature on state estimation of Boolean control networks (BCNs), it is almost assumed that the measurements are received without delay. However, in practice, measurements are always received with delay. This means that the received measurements may contain information about the previous state of the BCN. We study the optimal state estimation issue of BCNs with stochastic disturbances coming from measurements with random delay in this paper. Two types of random delay in measurements are considered. The first type is that the received measurements with delay or loss, and the probability distribution of the received measurement under different delay values is given. The second type is that the delay process follows a finite‐state Markov chain. For each type of the measurements, a method is put forward to compute the conditional probability distribution vector (CPDV) of the state through some input and output observations. After that, the state of a BCN can be estimated by minimizing the conditional mean squared deviation, where the difference between the estimated value and the real state is measured by the Euclidean distance. Moreover, with the purpose of estimating the state of a large‐scale BCN with stochastic disturbances without too much computational complexity, we transform the large‐scale BCN into a size‐reduced BCN and then obtain the optimal state estimation of the large‐scale BCN by estimating the state of the size‐reduced BCN. Since sampled measurements can sometimes be transformed into the second type of measurements with random delay, the method proposed here is also applicable for estimating the state of a BCN subject to sampled measurements.