Optimal Estimation in UDP-Like Networked Control Systems With Intermittent Inputs: Stability Analysis and Suboptimal Filter Design

We investigate the optimal estimation problem in lossy networked control systems where the control packets are randomly dropped without acknowledgment to the estimator. Most existing results for this setup are concerned with the design of controller, while the optimal estimation and its performance evaluation have been rarely treated. In this paper, we show that, unlike many other cases such as intermittent observations or TCP-like systems, the system state follows a Gaussian mixture distribution with exponentially increasing terms, which leads to a Gaussian sum filter-based optimal estimation. We develop an auxiliary estimator method to establish necessary and sufficient conditions for the stability of the mean estimation error covariance matrices. It is revealed that the stability is independent of the packet loss rate, and is not affected by the lack of acknowledgment. A suboptimal filtering algorithm with improved computational efficiency is then developed. Numerical examples and simulations are employed to illustrate the theoretical results.