Optimal Control of Multi-Agent Systems with Processing Delays

TL;DR

This paper derives explicit optimal control laws for multi-agent linear systems with fixed communication delays, providing a closed-form solution and efficient implementation under LQG assumptions.

Contribution

It presents the first explicit closed-form solution for decentralized control with delays in a multi-agent setting under LQG assumptions.

Findings

Explicit optimal decentralized controller derived

Solution handles fixed communication delays exactly

Controllers are efficiently implementable using standard LTI and FIR components

Abstract

In this article, we consider a cooperative control problem involving a heterogeneous network of dynamically decoupled continuous-time linear plants. The (output-feedback) controllers for each plant may communicate with each other according to a fixed and known transitively closed directed graph. Each transmission incurs a fixed and known time delay. We provide an explicit closed-form expression for the optimal decentralized controller and its associated cost under these communication constraints and standard linear quadratic Gaussian (LQG) assumptions for the plants and cost function. We find the exact solution without discretizing or otherwise approximating the delays. We also present an implementation of each sub-controller that is efficiently computable, and is composed of standard finite-dimensional linear time-invariant (LTI) and finite impulse response (FIR) components, and has an intuitive observer-regulator architecture reminiscent of the classical separation principle.