Output-Feedback System Level Synthesis via Dynamic Programming

TL;DR

This paper introduces a dynamic programming approach to output-feedback System Level Synthesis, significantly improving computational efficiency and scalability for large-scale control problems.

Contribution

It reformulates output-feedback SLS as a control problem solvable by dynamic programming, and proposes an approximation algorithm for faster solutions with comparable results.

Findings

DP achieves up to 7x faster solutions than convex programming.

Approximation algorithm reduces runtime by 42% to 68%.

Method scales well with large system dimensions and horizons.

Abstract

System Level Synthesis (SLS) allows us to construct internally stabilizing controllers for large-scale systems. However, solving large-scale SLS problems is computationally expensive and the state-of-the-art methods consider only state feedback; output feedback poses additional challenges because the constraints are no longer uniquely row or column separable. We exploit the structure of the output-feedback SLS problem by vectorizing the multi-sided matrix multiplications in the SLS optimization constraints, which allows us to reformulate it as a discrete-time control problem and solve using two stages of dynamic programming (DP). Additionally, we derive an approximation algorithm that offers a faster runtime by partially enforcing the constraints, and show that this algorithm offers the same results. DP solves SLS up to $7$ times faster, with an additional 42% to 68% improvement using the approximation algorithm, than a convex program solver, and scales with large state dimensions and finite impulse response horizon.