Estimation and LQG Control Over Unreliable Network With Acknowledgment Randomly Lost

In this paper, we study the state estimation and optimal control [i.e., linear quadratic Gaussian (LQG) control] problems for networked control systems in which control inputs, observations, and packet acknowledgments (ACKs) are randomly lost. The packet ACK is a signal that is transmitted from the actuator to notice the estimator the occurrence of control packet loss. For such systems, we obtain the optimal estimator, which is consisted of exponentially increasing terms. For the solvability of the LQG problem, we come to a conclusion that in general even the optimal LQG control exists, it is impossible and unnecessary to be obtained as its calculation is not only technically difficult but also computationally prohibitive. This issue motivates us to design a suboptimal LQG controller for the underlying systems. We first develop a suboptimal estimator by using the estimator gain in each term of the optimal estimator. Then we derive a suboptimal LQG controller and establish the conditions for stability of the closed-loop systems. Examples are given to illustrate the effectiveness and advantages of the proposed design scheme.