Discrete‐time linear quadratic gaussian control with input delay and Markovian packet dropouts

Abstract

This article investigates the finite horizon linear quadratic gaussian (LQG) control problem for networked control systems with two‐way Markovian packet dropouts and input delay, where packet dropouts occur from the sensor to the estimator and from the controller to the actuator, and delay occurs from the controller to the actuator. The novelty of this work lies in providing a complete solution for the optimal control problem subject to two‐way Markovian packet dropouts and input delay. The contributions of this article are as follows: first, by applying the maximum principle to the discrete‐time linear systems and the quadratic cost function involving input delay and Markovian packet dropouts, a solution to the forward and backward stochastic difference equations (FBSDEs) is derived. Second, a sufficient and necessary condition for the optimal control problem is obtained by decoupling the coupled Riccati equations. Finally, the explicit solution of the optimal controller is presented based on the complete square method. Numerical examples are provided to demonstrate the validity of the theoretical results.