Optimal Local and Remote Controls of Multiple Systems with Multiplicative Noises and Unreliable Uplink Channels

TL;DR

This paper develops optimal control strategies for a networked control system with multiple subsystems affected by multiplicative noise and unreliable uplink channels, using advanced stochastic control techniques to handle asymmetric information.

Contribution

It introduces a novel approach to solve the LQ control problem in systems with multiplicative noise and unreliable communication, establishing the separation principle under these conditions.

Findings

Derived necessary and sufficient conditions for optimal control using G-FBSDEs.

Proposed a new method to decouple complex difference equations.

Verified the separation principle for systems with packet dropouts and multiplicative noise.

Abstract

In this paper, the optimal local and remote linear quadratic (LQ) control problem is studied for a networked control system (NCS) which consists of multiple subsystems and each of which is described by a general multiplicative noise stochastic system with one local controller and one 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 Pontyagin 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). Furthermore, by proposing a new method to decouple the G-FBSDEs and introducing new coupled Riccati equations (CREs), the optimal control strategies are derived where we verify that the separation principle holds for the multiplicative noise NCSs with packet dropouts. This paper can be seen as an important contribution to the optimal control problem with asymmetric information structures.