State estimation over non-acknowledgment networks with Markovian packet dropouts

Abstract

In this paper, we investigate state estimation for systems with packet dropouts. According to whether there are acknowledgment (ACK) signals sent by the actuator to the estimator indicating the status of control packet dropouts or not, the systems are classified into two types: ACK systems, those with ACK signals, and non-ACK (NACK) systems, those without. We first obtain the optimal estimator (OE) for NACK systems with Markovian packet dropouts. However, the number of the components in the OE grows exponentially, making its stability analysis complicated and its computation time-consuming. Therefore, we proceed to design a computationally efficient approximate optimal estimator (AOE) using a relative-entropy-based approach. We prove that the proposed AOE has the same stability as the OE. We show that, even the separation principle does not hold for NACK systems, the stability of the OE can also be investigated separately; and discover that the OE for an NACK system has the same stability as the OE for the corresponding ACK system, even their structures are quite different. Finally, for strongly observable NACK systems, we establish a necessary and sufficient condition for the stability of the OE and the AOE.