# A System Level Approach to Controller Synthesis

arXiv: https://arxiv.org/abs/1610.04815 · HTML: https://mlsanity.com/paper/1610.04815/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2016.

## Built on by (most cited first, 9 of 9)

- [Online Control of Unknown Time-Varying Dynamical Systems](https://mlsanity.com/paper/2202.07890/) (2022)
- [Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2203.11812/) (2022)
- [Learning to Boost the Performance of Stable Nonlinear Systems](https://mlsanity.com/paper/2405.00871/) (2024)
- [Online Convex Optimization with Unbounded Memory](https://mlsanity.com/paper/2210.09903/) (2022)
- [Optimal Competitive-Ratio Control](https://mlsanity.com/paper/2206.01782/) (2022)
- [Distributionally Robust PAC-Bayesian Control](https://mlsanity.com/paper/2604.10588/) (2026)
- [Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part II: Theoretical & Computational Results](https://mlsanity.com/paper/2208.03625/) (2022)
- [Follow the Clairvoyant: an Imitation Learning Approach to Optimal Control](https://mlsanity.com/paper/2211.07389/) (2022)
- [PAC-Bayesian Certificates for Quadratic Closed-Loop Control](https://mlsanity.com/paper/2606.28281/) (2026)

## Abstract (arXiv)

Biological and advanced cyberphysical control systems often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation. Fortunately, the corresponding plants and performance requirements are also sparse and structured, and this must be exploited to make constrained controller design feasible and tractable. We introduce a new "system level" (SL) approach involving three complementary SL elements. System Level Parameterizations (SLPs) generalize state space and Youla parameterizations of all stabilizing controllers and the responses they achieve, and combine with System Level Constraints (SLCs) to parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization, generalizing quadratic invariance (QI). SLPs also lead to a generalization of detectability and stabilizability, suggesting the existence of a rich separation structure, that when combined with SLCs, is naturally applicable to structurally constrained controllers and systems. We further provide a catalog of useful SLCs, most importantly including sparsity, delay, and locality constraints on both communication and computing internal to the controller, and external system performance. The resulting System Level Synthesis (SLS) problems that arise define the broadest known class of constrained optimal control problems that can be solved using convex programming. An example illustrates how this system level approach can systematically explore tradeoffs in controller performance, robustness, and synthesis/implementation complexity.