Optimal Estimation and Control for Lossy Network: Stability, Convergence, and Performance

Abstract

Abstract-In this paper, we study the problems of optimal estimation and control, i.e., the linear quadratic Gaussian (LQG) control, for systems with packet losses but without acknowledgment. Such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses. For such system, which is usually called as a User Datagram Protocol (UDP)-like system, the optimal estimation is nonlinear and its calculation is time-consuming, making its corresponding optimal LQG problem complicated. We first propose two conditions: 1) the sensor has some computation abilities; and 2) the control command, exerted to the plant, is known to the sensor. For a UDP-like system satisfying these two conditions, we derive the optimal estimation. By constructing the finite and infinite product probability measure spaces for the estimation error covariances (EEC), we give the stability condition for the expected EEC, and show the existence of a measurable function to which the EEC converges in distribution, and propose some practical methods to evaluate the estimation performance. Finally, the LQG controllers are derived, and the conditions for the mean square stability of the closed-loop system are established.

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

“…Although some theoretical problems have been solved, there still exist many issues for UDP-like systems, such as designing efficient sub-optimal/approximate estimators and controllers, considering Markovian or correlated packet losses in communication channels, and studying consensus problems [37] for multi-agent UDP-like systems. Investigating estimation and control problems for UDP-like systems equipped with devices having computational ability or intelligent strategies-such as eventtrigger schemes [22], smart sensors [17], and network relays [12]-may obtain some interesting results.…”

“…Proof: For Gaussian mixture pdfs, by applying (3) to p(x k |G k−1 ) and p(x k |G k ), the optimal estimator can be readily obtained as in (17). 2…”

“…Thus, in the following lemma the mathematical expectation is taken with respect to G k−1 . (2) and (17).…”

State estimation for a networked control system with packet delay, packet dropouts, and uncertain observation in S‐E and C‐A channels

“…In Reference 26 bounded packet delay and multiple dropouts in the S‐E and C‐A channels is considered, and a minimum variance‐based linear filter with correlated process and measurement noise is designed, which depends on the probability of delay and dropout. NCS with packet loss in both S‐E and C‐A channels is studied, where the loss in both channels is modeled using Bernoulli distributed random variables 27 . Recursive estimation for systems with multiplicative noises, random delays, and multiple packet dropouts is proposed in Reference 28.…”

State estimation over non-acknowledgment networks with Markovian packet dropouts

“…That is why the majority of estimation-related issues for ACK systems can be investigated by using the model in Fig. 1 protocol (UDP)) [15,25], where TCP has an ACK mechanism for packet dropouts while UDP has not [6]. Under TCP, the sender retransmits the dropped packets until acknowledged by the receiver that the packet has been successfully received.…”