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Classical linear quadratic (LQ) control centers around linear time-invariant(LTI) systems, where the control-state pairs introduce a quadratic cost withtime-invariant parameters. Recent advancement in online optimization andcontrol has provided novel tools to study LQ problems that are robust totime-varying cost parameters. Inspired by this line of research, we study thedistributed online LQ problem for identical LTI systems. Consider a multi-agentnetwork where each agent is modeled as an LTI system. The LTI systems areassociated with decoupled, time-varying quadratic costs that are revealedsequentially. The goal of the network is to make the control sequence of allagents competitive to that of the best centralized policy in hindsight,captured by the notion of regret. We develop a distributed variant of theonline LQ algorithm, which runs distributed online gradient descent with aprojection to a semi-definite programming (SDP) to generate controllers. Weestablish a regret bound scaling as the square root of the finite time-horizon,implying that agents reach consensus as time grows. We further providenumerical experiments verifying our theoretical result.

Distributed Online Linear Quadratic Control for Linear Time-invariant Systems