Robust Performance Guarantees for System Level Synthesis

TL;DR

This paper extends the system level synthesis framework to include bounded causal linear operators, providing convex conditions for robust performance that incorporate delays, sparsity, and locality, enabling scalable distributed control solutions.

Contribution

It introduces a novel connection between robust system level synthesis and classical robust control, allowing for convex constraints that handle delays and sparsity in large-scale distributed systems.

Findings

Established convex conditions for robust performance with bounded linear uncertainties.

Demonstrated incorporation of delay, sparsity, and locality constraints.

Provided the first robust guarantees for distributed control systems.

Abstract

We generalize the system level synthesis framework to systems defined by bounded causal linear operators, and use this parameterization to make connections between robust system level synthesis and classical results from the robust control literature. In particular, by leveraging results from L1 robust control, we show that necessary and sufficient conditions for robust performance with respect to causal bounded linear uncertainty in the system dynamics can be translated into convex constraints on the system responses. We exploit this connection to show that these conditions naturally allow for the incorporation of delay, sparsity, and locality constraints on the system responses and resulting controller implementation, allowing these methods to be applied to large-scale distributed control problems -- to the best of our knowledge, these are the first such robust performance guarantees for distributed control systems.