System Level Synthesis for Affine Control Policies: Model Based and Data-Driven Settings

There is an increasing need for effective control of systems with complex dynamics, particularly through data-driven approaches. System Level Synthesis (SLS) has emerged as a powerful framework that facilitates the control of large-scale systems while accounting for model uncertainties. SLS approaches are currently limited to linear systems and time-varying linear control policies, thus limiting the class of achievable control strategies. We introduce a novel closed-loop parameterization for time-varying affine control policies, extending the SLS framework to a broader class of systems and policies. We show that the closed-loop behavior under affine policies can be equivalently characterized using past system trajectories, enabling a fully data-driven formulation. This parameterization seamlessly integrates affine policies into optimal control problems, allowing for a closed-loop formulation of general Model Predictive Control (MPC) problems. To the best of our knowledge, this is the first work to extend SLS to affine policies in both model-based and data-driven settings, enabling an equivalent formulation of MPC problems using closed-loop maps. We validate our approach through numerical experiments, demonstrating that our model-based and data-driven affine SLS formulations achieve performance on par with traditional model-based MPC.

💡 Research Summary

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The paper addresses a fundamental limitation of the existing System Level Synthesis (SLS) framework, which has so far been confined to linear time‑varying (LTV) policies applied to linear systems. In many practical control scenarios—particularly Model Predictive Control (MPC) with state and input constraints—the optimal control law is piecewise‑affine, and a purely linear policy cannot capture this structure. To overcome this gap, the authors propose a novel closed‑loop parameterization that accommodates time‑varying affine policies.

The key idea is to decompose the control input at each time step into a linear feedback term and an explicit affine term:

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