Interacting Multiple Model Estimator for Networked Control Systems: Stability, Convergence, and Performance

In this paper, we study the interacting multiple model (IMM) estimator for networked control systems with packet loss but without packet acknowledgment (ACK). The ACK is a signal sent by the actuator to inform the estimator of whether control packets are lost or not. A system with ACK is usually called a transmission control protocol (TCP) like system; otherwise, it is called a user datagram protocol (UDP) like system. We show that the stability of the IMM estimator for UDP-like systems is determined by the observation packet arrival rate (p.a.r.) and is independent of the control p.a.r. and control inputs. The IMM estimator is stable if the observation p.a.r. is greater than a critical value. We show that this critical value is the same as the critical value for the stability of the optimal estimator for its corresponding TCP-like system. If control inputs eventually tend to zero, the error covariance of the IMM estimator converges to that of the optimal estimator for TCP-like systems. We characterize the impact of the control/observation p.a.r. and the control input on estimation performance. Finally, we prove that the average estimation performance of the IMM estimator approximates that of the optimal estimator within a finite bound, and is superior to that of the linear minimum mean square error estimator.