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Optimal filtering and control for wireless networked closed‐loop control systems

This article studies the optimal filtering and control for wireless networked control systems (WNCSs). In WNCSs, packets may be lost in both control and feedback channels and user datagram protocol is usually used to improve the performance of the real‐time control. Relevant literature indicates that the conventional optimal filtering for such a system cannot be applied in practice due to the complex calculation with Gaussian mixtures. This paper proposes a novel scheme to realize the optimal filtering and the linear quadratic Gaussian control for WNCSs, in which the controlled node performs a local estimation and the remote‐control node performs the final estimation and control, and a synchronization of two estimators is guaranteed by a communication mechanism. An optimal filtering algorithm is developed, the stability condition of the filtering error covariance is obtained, optimal finite‐horizon and infinite‐horizon control are derived, and the stability of the closed‐loop control system is proved. Numerical simulations show the validity and feasibility of the theoretical results.