Optimal Local and Remote Controls of Networked Systems: Multiplicative Noise Case

In this paper, the linear quadratic (LQ) optimal control problem is studied for multiplicative noise networked control systems (MN-NCSs) with two controllers of different information structures. The challenges and difficulties of the considered problems are twofold: Firstly, the system dynamics is described by a multiplicative noise system and regulated by a local control and a remote control, which may cause separation principle to fail. Besides, by adopting the Pontryagin maximum principle, the local controller can not be solved from the equilibrium conditions directly. To overcome these difficulties, an innovative approach is adapted to solve the forward and backward stochastic difference equations (FBSDEs). It is verified that the separation principle holds, and the optimal local control and optimal remote control are derived based on coupled Riccati equations.