System level synthesis

Anderson, James; Doyle, John C.; Low, Steven H.; Matni, Nikolai

doi:10.1016/j.arcontrol.2019.03.006

Cited by 154 publications

(249 citation statements)

References 60 publications

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“…Instead, both SLP and IOP do not require to compute a doublycoprime factorization, but have explicit affine constraints for achievable closed-loop responses. Since the decision variables in constraints (8a)-(8c) and (12a)-(12c) are infinite dimensional, there is no immediately efficient numerical method for solving (10) or (14). The Ritz approximation [3, Chapter 15] is one method for solving infinite dimensional optimization problems.…”

Section: Statementmentioning

confidence: 99%

“…In [5], the authors introduced a general framework of system-level synthesis (SLS), which defines "the broadest known class of constrained optimal control problems that can be solved using convex programming" (cf. [10]). Thanks to the full equivalence in Theorems 1-3, we can show that 1) any SLS problem can be equivalently formulated in the Youla or input-output framework, 2) any convex SLS can be addressed by solving a convex problem in terms of Youla parameter Q or input-output parameters Y, U, W, Z.…”

Section: B Convex System-level Synthesismentioning

confidence: 99%

“…B. Example 1 in [5], [10] Consider the following optimal control problem, which is Example 1 in [5], [10],…”

Section: A Simplified Parameterizations For State Feedbackmentioning

confidence: 99%

See 2 more Smart Citations

On the Equivalence of Youla, System-Level, and Input–Output Parameterizations

Zheng

Furieri

Papachristodoulou

et al. 2021

IEEE Trans. Automat. Contr.

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A convex parameterization of internally stabilizing controllers is fundamental for many controller synthesis procedures. The celebrated Youla parameterization relies on a doublycoprime factorization of the system, while the recent system-level and input-output characterizations require no doubly-coprime factorization but a set of equality constraints for achievable closed-loop responses. In this paper, we present explicit affine mappings among Youla, system-level and input-output parameterizations. Two direct implications of the affine mappings are 1) any convex problem in Youla, system level, or input-output parameters can be equivalently and convexly formulated in any other one of these frameworks, including the convex system-level synthesis (SLS); 2) the condition of quadratic invariance (QI) is sufficient and necessary for the classical distributed control problem to admit an equivalent convex reformulation in terms of Youla, system-level, or input-output parameters.

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Section: Statementmentioning

confidence: 99%

Section: B Convex System-level Synthesismentioning

confidence: 99%

See 1 more Smart Citation

On the Equivalence of Youla, System-Level, and Input–Output Parameterizations

Zheng

Furieri

Papachristodoulou

et al. 2021

IEEE Trans. Automat. Contr.

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“…2) System Level Synthesis: Here we provide a very brief overview of the system level synthesis framework for distributed control. This paper is intended to be self contained, but the reader is referred to [1], [13] for a more complete picture of both theory and computation. We consider a linear time-invariant plant model of the form x(k + 1) = Ax(k) + Bu(k) + w(k), where x(k), w(k) ∈ R n are the state and noise vectors at time k, and u(k) ∈ R m is the control action at time k. The control synthesis problem is to design a dynamic state-feedback policy u = Kx.…”

Section: A Preliminariesmentioning

confidence: 99%

System Level Synthesis with State and Input Constraints

Chen

Anderson

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper addresses the problem of designing distributed controllers with state and input constraints in the System Level Synthesis (SLS) framework. Using robust optimization, we show how state and actuation constraints can be incorporated into the SLS structure. Moreover, we show that the dual variable associated with the constraint has the same sparsity pattern as the SLS parametrization, and therefore the computation distributes using a simple primal-dual algorithm. We provide a stability analysis for SLS design with input saturation under the Internal Model Control (IMC) framework. We show that the closed-loop system with saturation is stable if the controller has a gain less than one. In addition, a saturation compensation scheme that incorporates the saturation information is proposed which improves the naive SLS design under saturation.Note that (2) imposes the constraint Φ x [1] = I.

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“…The recently developed System Level Synthesis (SLS) framework addresses this challenge by shifting the optimization from the space of available controllers to the space of achievable system closed-loop maps [7]. In doing so, it allows the problem to be decomposed into sub-problems to be solved in parallel, resulting in a synthesis procedure with O(1) complexity [8].…”

Section: Introductionmentioning

confidence: 99%

Separating Controller Design from Closed-Loop Design: A New Perspective on System-Level Controller Synthesis

2020

2020 American Control Conference (ACC)

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We show that given a desired closed-loop response for a system, there exists an affine subspace of controllers that achieve this response. By leveraging the existence of this subspace, we are able to separate controller design from closed-loop design by first synthesizing the desired closed-loop response and then synthesizing a controller that achieves the desired response. This is a useful extension to the recently introduced System Level Synthesis framework, in which the controller and closed-loop response are jointly synthesized and we cannot enforce controller-specific constraints without subjecting the closed-loop map to the same constraints. We demonstrate the importance of separating controller design from closed-loop design with an example in which communication delay and locality constraints cause standard SLS to be infeasible. Using our new two-step procedure, we are able to synthesize a controller that obeys the constraints while only incurring a 3% increase in LQR cost compared to the optimal LQR controller.

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System level synthesis

Cited by 154 publications

References 60 publications

On the Equivalence of Youla, System-Level, and Input–Output Parameterizations

On the Equivalence of Youla, System-Level, and Input–Output Parameterizations

System Level Synthesis with State and Input Constraints

Separating Controller Design from Closed-Loop Design: A New Perspective on System-Level Controller Synthesis

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