115 research outputs found
Sample Complexity of the Robust LQG Regulator with Coprime Factors Uncertainty
This paper addresses the end-to-end sample complexity bound for learning the
H2 optimal controller (the Linear Quadratic Gaussian (LQG) problem) with
unknown dynamics, for potentially unstable Linear Time Invariant (LTI) systems.
The robust LQG synthesis procedure is performed by considering bounded additive
model uncertainty on the coprime factors of the plant. The closed-loop
identification of the nominal model of the true plant is performed by
constructing a Hankel-like matrix from a single time-series of noisy finite
length input-output data, using the ordinary least squares algorithm from
Sarkar et al. (2020). Next, an H-infinity bound on the estimated model error is
provided and the robust controller is designed via convex optimization, much in
the spirit of Boczar et al. (2018) and Zheng et al. (2020a), while allowing for
bounded additive uncertainty on the coprime factors of the model. Our
conclusions are consistent with previous results on learning the LQG and LQR
controllers.Comment: Minor Edits on closed loop identification, 30 pages, 2 figures, 3
algorithm
System Level Synthesis
This article surveys the System Level Synthesis framework, which presents a
novel perspective on constrained robust and optimal controller synthesis for
linear systems. We show how SLS shifts the controller synthesis task from the
design of a controller to the design of the entire closed loop system, and
highlight the benefits of this approach in terms of scalability and
transparency. We emphasize two particular applications of SLS, namely
large-scale distributed optimal control and robust control. In the case of
distributed control, we show how SLS allows for localized controllers to be
computed, extending robust and optimal control methods to large-scale systems
under practical and realistic assumptions. In the case of robust control, we
show how SLS allows for novel design methodologies that, for the first time,
quantify the degradation in performance of a robust controller due to model
uncertainty -- such transparency is key in allowing robust control methods to
interact, in a principled way, with modern techniques from machine learning and
statistical inference. Throughout, we emphasize practical and efficient
computational solutions, and demonstrate our methods on easy to understand case
studies.Comment: To appear in Annual Reviews in Contro
System level synthesis
This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty – such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies
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