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Computing Robust Controlled Invariant Sets of Linear Systems

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Matthias Rungger, Paulo Tabuada

Optimization and Control · Submitted 4 Jan 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation of the maximal robust controlled invariant set, while the second method provides an inner approximation.

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arXiv ID1601.00416 (version 2)
Pith IDWYVIPAXZ, Pith's permanent record of this paper and its review
CitationMatthias Rungger, Paulo Tabuada. "Computing Robust Controlled Invariant Sets of Linear Systems." arXiv:1601.00416 (2016). https://pith.science/paper/WYVIPAXZ
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,932 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.81 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation of the maximal robust controlled invariant set, while the second method provides an inner approximation. The outer approximation scheme is $\delta$-complete, given that the constraint sets are formulated as finite unions of polytopes.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. contribution 0.78 0.89 0.13 asserted 0.99
s1 The first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation of the maximal robust controlled invariant set, while the second method provides an inner approximation. contribution 0.61 0.89 0.44 asserted 1.00
s2 The outer approximation scheme is $\delta$-complete, given that the constraint sets are formulated as finite unions of polytopes. result 0.83 0.79 0.20 asserted 0.99

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.96.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation of the maximal robust controlled invariant set, while the second method provides an inner approximation. The outer approximation scheme is $\delta$-complete, given that the constraint sets are formulated as finite unions of polytopes.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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