Necessary and Sufficient Condition of Optimal Control for Networked Control Systems with Markovian Packet Dropouts

This paper considers optimal control problem for networked control systems (NCSs) with Markovian packet dropouts. Since previous literatures generally consider the one-way Markovian packet dropouts, i.e., from the sensor to the estimator or from the controller to the actuator. To make a further study of this issue, we aim to give the complete solution to the control problem of the two-way Markovian packet dropouts, i.e., from the sensor to the estimator and from the controller to the actuator. Firstly, by applying the Pontryagin's maximum principle and mathematical induction method, a solution to the forward and backward stochastic difference equations (FBSDEs) is derived. Secondly, in virtue of the solution to the FBSDEs, we obtain the necessary and sufficient condition for the optimal control problem. Thirdly, the optimal controller is given based on the complete square method. Finally, numerical examples are proposed to illustrate the effectiveness of the theoretical results.