From System Level Synthesis to Robust Closed-loop Data-Enabled Predictive Control

Lian, Yingzhao; Jones, Colin N.

doi:10.1109/cdc45484.2021.9683429

Cited by 11 publications

(14 citation statements)

References 16 publications

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“…for all γ ∈ R. Recall that by Assumption 1, M 22 ≤ 0. This implies that M 22 Ẑ = 0, for otherwise there exists a sufficiently large γ ∈ R violating (14). We have thus proven that ker N 22 ⊆ ker M 22 , equivalently, im M 22 ⊆ im N 22 .…”

Section: The Matrix Finsler's Lemmamentioning

confidence: 67%

“…Both paradigms have a long history, but data-driven control has recently witnessed a renewed surge of interest, partly because of the widespread availability of data and the successes of machine learning algorithms. We mention contributions to data-driven optimal control [1]- [4], predictive control [5]- [8] and robust tracking control [9], nonlinear control [10]- [12] and system level synthesis [13], [14].…”

Section: Introductionmentioning

confidence: 99%

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A Matrix Finsler's Lemma with Applications to Data-Driven Control

Waarde¹,

Camlibel²

2021

Preprint

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In a recent paper it was shown how a matrix S-lemma can be applied to construct controllers from noisy data. The current paper complements these results by proving a matrix version of the classical Finsler's lemma. This matrix Finsler's lemma provides a tractable condition under which all matrix solutions to a quadratic equality also satisfy a quadratic inequality. We will apply this result to bridge known datadriven control design techniques for both exact and noisy data, thereby revealing a more general theory. The result is also applied to data-driven control of Lur'e systems.

show abstract

Section: The Matrix Finsler's Lemmamentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

A Matrix Finsler's Lemma with Applications to Data-Driven Control

Waarde¹,

Camlibel²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…for all γ ∈ R. Recall that by Assumption 1), M 22 ≤ 0. This implies that M 22 Ẑ = 0, for otherwise there exists a sufficiently large γ ∈ R violating (14). We have thus proven that ker N 22 ⊆ ker M 22 , equivalently, im…”

mentioning

confidence: 68%

A Matrix Finsler’s Lemma with Applications to Data-Driven Control

Waarde

Camlibel

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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“…Then we can adjust Algorithm 1 to Problem (18) to enable dropping constraints. First let us rewrite (10) as:…”

Section: Convergence Of Algorithmmentioning

confidence: 99%

Automatic scenario generation for efficient solution of robust optimal control problems

Zagórowska¹,

Falugi²,

O’Dwyer³

et al. 2023

Preprint

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Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time-varying uncertainty. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric and timevarying uncertainty. By iteratively adding interim worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst-case constraint violations. In particular, we present examples where local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time-varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all 2 14+3×192 extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time-varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive.

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From System Level Synthesis to Robust Closed-loop Data-Enabled Predictive Control

Cited by 11 publications

References 16 publications

A Matrix Finsler's Lemma with Applications to Data-Driven Control

A Matrix Finsler's Lemma with Applications to Data-Driven Control

A Matrix Finsler’s Lemma with Applications to Data-Driven Control

Automatic scenario generation for efficient solution of robust optimal control problems

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