Data-Driven System Level Synthesis

• URL: http://arxiv.org/abs/2011.10674v3
• Date: Sat, 6 Mar 2021 19:42:49 GMT
• Title: Data-Driven System Level Synthesis
• Authors: Anton Xue and Nikolai Matni
• Abstract summary: We show that optimization problems over system-responses can be posed using only libraries of past system trajectories. We first consider the idealized setting of noise free trajectories, and show an exact equivalence between traditional and data-driven SLS. We then show that in the case of a system driven by process noise, tools from robust SLS can be used to characterize the effects of noise on closed-loop performance.
• Score: 2.335152769484957
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish data-driven versions of the System Level Synthesis (SLS) parameterization of achievable closed-loop system responses for a linear-time-invariant system over a finite-horizon. Inspired by recent work in data-driven control that leverages tools from behavioral theory, we show that optimization problems over system-responses can be posed using only libraries of past system trajectories, without explicitly identifying a system model. We first consider the idealized setting of noise free trajectories, and show an exact equivalence between traditional and data-driven SLS. We then show that in the case of a system driven by process noise, tools from robust SLS can be used to characterize the effects of noise on closed-loop performance, and further draw on tools from matrix concentration to show that a simple trajectory averaging technique can be used to mitigate these effects. We end with numerical experiments showing the soundness of our methods.

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