On stability and convergence of optimal estimation for networked control systems with dual packet losses without acknowledgment

This paper studies the optimal state estimation problem for networked control systems with control and observation packet losses but without packet acknowledgment (ACK). The packet ACK is a signal sent by the actuator to inform the estimator whether control packets are lost or not. Systems with packet ACK are usually called transmission control protocol (TCP)-like systems, and those without ACK are named user datagram protocol (UDP)-like systems. For UDP-like systems, the optimal estimator is derived and it is consisted of an exponentially increasing number of terms. By developing an auxiliary estimator, it is shown that there exists a critical observation packet arrival rate determining the stability of the expected EC (EEC), and it is identical to its counterpart for TCP-like systems. It is revealed that whether there is packet ACK or not has no effect on the stability of the EEC. Furthermore, under some conditions the EEC converges exponentially.