Further results on optimal local and remote control with packet losses and transmission delay

Abstract

In this article, the finite horizon optimal local and remote control (LRC) problem is further investigated for the case that both the packet losses (PL) and the transmission delays (TD) occur over the unreliable uplink channel from the local controller to the remote controller. In terms of the variational technique and the dynamic programming approach, the LRC problem with PL and TD is solved for the first time. The results derived in this article are innovative in the following aspects: Firstly, the necessary and sufficient solvability conditions are developed using the convex variational technique, illustrating that the solvability of the LRC problem is equivalent to the solvability of the forward and backward stochastic differential equations (FBSDEs). Secondly, by proposing an innovative hierarchical control technique and using the optimality principle of dynamic programming, the explicit optimal linear LRC is derived in terms of the completing square approach. Finally, the derived results of this article are illustrated by a numerical example.