Jointly Optimal Local and Remote Controls for Networked Multiple Systems With Multiplicative Noises and Unreliable Uplink Channels

Abstract

This article investigates the finite horizon jointly optimal local and remote linear quadratic (LQ) control problem for a networked control system (NCS) with multiple subsystems. Each subsystem is governed by a general multiplicative noise stochastic system and is equipped with both a local controller and a remote controller. Due to the unreliable uplink channels, the remote controller can only access unreliable state information of all subsystems, while the downlink channels from the remote controller to the local controllers are perfect. The difficulties of the LQ control problem for such a system arise from the different information structures of the local controllers and the remote controller. By developing the Pontryagin maximum principle, the necessary and sufficient solvability conditions are derived, which are based on the solution to a group of forward and backward difference equations (G-FBSDEs). The G-FBSDEs, however, cannot be decoupled by existing techniques. By introducing a group of new auxiliary information filtration and utilizing the orthogonal decomposition method, the G-FBSDEs is thus solved, and the decoupling method is novel. Furthermore, based on the solution to new asymmetric coupled Riccati equations, the optimal control strategies are derived where we verify that the separation principle holds for the multiplicative noise NCSs with packet dropouts.