Agent-level optimal LQG control of dynamically decoupled systems with processing delays

TL;DR

This paper derives explicit optimal decentralized LQG controllers for dynamically decoupled systems with fixed communication delays, revealing their observer-regulator structure and information-sharing signals.

Contribution

It provides the first closed-form solutions for optimal decentralized control with processing delays in decoupled systems under LQG assumptions.

Findings

Explicit closed-form optimal controllers derived

Controllers have observer-regulator architecture with LTI and FIR blocks

Characterization of inter-controller transmitted signals

Abstract

We consider the problem of controlling a set of dynamically decoupled plants where the plants' subcontrollers communicate with each other according to a fixed and known network topology. We assume the communication to be instantaneous but there is a fixed processing delay associated with incoming transmissions. We provide explicit closed-form expressions for the optimal decentralized controller under these communication constraints and using standard LQG assumptions for the plants and cost function. Although this problem is convex, it is challenging due to the irrationality of continuous-time delays and the decentralized information-sharing pattern. We show that the optimal subcontrollers each have an observer-regulator architecture containing LTI and FIR blocks and we characterize the signals that subcontrollers should transmit to each other across the network.