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In this paper, the filtering issues are investigated for wireless networked control systems (WNCSs) with Markovian packet losses. In WNCSs, Markovian packet losses often occur in both control and feedback channels, and User Datagram Protocol (UDP) is usually used to ensure real-time control and energy saving. First, the optimal filtering algorithm for WNCSs with Markovian packet losses is obtained. However, it cannot be applied in practice as its running time increases exponentially with time. Then a computationally efficient filtering algorithm is developed by approximating the probability density function of the estimated value to a Gaussian distribution, where the approximation is obtained by minimising the Kullback-Leibler divergence (KLD). Finally, the upper and lower bounds of the performance of the KLD-based approximate filter and sufficient conditions of its stability are obtained. Numerical examples are given to verify the effectiveness of the theoretical results.

Efficient filtering based on Kullback-Leibler divergence for wireless networked control systems with Markovian packet losses