Separating Controller Design from Closed-Loop Design: A New Perspective on System-Level Controller Synthesis

TL;DR

This paper introduces a novel approach to system-level controller synthesis that separates the design of the closed-loop response from the controller, enabling the incorporation of constraints more effectively and demonstrating practical benefits.

Contribution

It proposes a two-step synthesis method that separates closed-loop response design from controller synthesis, extending the System Level Synthesis framework.

Findings

Enables controller design with communication delay and locality constraints.

Achieves near-optimal LQR cost with constraints.

Demonstrates feasibility where standard SLS fails.

Abstract

We show that given a desired closed-loop response for a system, there exists an affine subspace of controllers that achieve this response. By leveraging the existence of this subspace, we are able to separate controller design from closed-loop design by first synthesizing the desired closed-loop response and then synthesizing a controller that achieves the desired response. This is a useful extension to the recently introduced System Level Synthesis framework, in which the controller and closed-loop response are jointly synthesized and we cannot enforce controller-specific constraints without subjecting the closed-loop map to the same constraints. We demonstrate the importance of separating controller design from closed-loop design with an example in which communication delay and locality constraints cause standard SLS to be infeasible. Using our new two-step procedure, we are able to synthesize a controller that obeys the constraints while only incurring a 3% increase in LQR cost compared to the optimal LQR controller.