Filtering for networked control systems with single/multiple measurement packets subject to multiple-step measurement delays and multiple packet dropouts

The minimum-variance filtering problem in networked control systems, where both random measurement transmission delays and packet dropouts may occur, is investigated in this article. Instead of following the many existing results that solve the problem by using probabilistic approaches based on the probabilities of the uncertainties occurring between the sensor and the filter, we propose a non-probabilistic approach by time-stamping the measurement packets. Both single-measurement and multiple measurement packets are studied. We also consider the case of burst arrivals, where more than one packet may arrive between the receiver's previous and current sampling times; the scenario where the control input is non-zero and subject to delays and packet dropouts is examined as well. It is shown that, in such a situation, the optimal state estimate would generally be dependent on the possible control input. Simulations are presented to demonstrate the performance of the various proposed filters.