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On the optimal control of non-expansive or passive systems

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Timothy H. Hughes

Systems and Control · Submitted 23 Mar 2017

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

The authors' main claim In this paper, we solve these optimal control problems without making any assumptions.

how it is stated · asserted 1.00 read the record →

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arXiv ID1703.08153 (version 2)
Pith IDDU7JW7XX, Pith's permanent record of this paper and its review
CitationTimothy H. Hughes. "On the optimal control of non-expansive or passive systems." arXiv:1703.08153 (2017). https://pith.science/paper/DU7JW7XX
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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, 4,884 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The positive-real and bounded-real lemmas solve two important linear-quadratic optimal control problems for passive and non-expansive systems, respectively. The lemmas assume controllability, yet a passive or non-expansive system can be uncontrollable. In this paper, we solve these optimal control problems without making any assumptions. In particular, we show how to extract the greatest possible amount of energy from a passive but not necessarily controllable system (e.g., a passive electric circuit) using state feedback. A complete characterisation of the set of solutions to the linear matrix inequalities in the positive-real and bounded-real lemmas is also obtained. In addition, we obtain necessary and sufficient conditions for a system to be non-expansive that augment the bounded-real condition with new conditions relevant to uncontrollable systems.

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 The positive-real and bounded-real lemmas solve two important linear-quadratic optimal control problems for passive and non-expansive systems, respectively. background 1.00 0.05 0.05 asserted 1.00
s1 The lemmas assume controllability, yet a passive or non-expansive system can be uncontrollable. gap 0.75 0.07 0.04 asserted 0.98
s2 In this paper, we solve these optimal control problems without making any assumptions. contribution 0.99 0.95 0.67 asserted 1.00
s3 In particular, we show how to extract the greatest possible amount of energy from a passive but not necessarily controllable system (e.g., a passive electric circuit) using state feedback. contribution 0.58 0.92 0.24 asserted 1.00
s4 A complete characterisation of the set of solutions to the linear matrix inequalities in the positive-real and bounded-real lemmas is also obtained. result 0.71 0.95 0.12 asserted 1.00
s5 In addition, we obtain necessary and sufficient conditions for a system to be non-expansive that augment the bounded-real condition with new conditions relevant to uncontrollable systems. result 0.74 0.96 0.14 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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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

The positive-real and bounded-real lemmas solve two important linear-quadratic optimal control problems for passive and non-expansive systems, respectively. The lemmas assume controllability, yet a passive or non-expansive system can be uncontrollable. In this paper, we solve these optimal control problems without making any assumptions. In particular, we show how to extract the greatest possible amount of energy from a passive but not necessarily controllable system (e.g., a passive electric circuit) using state feedback. A complete characterisation of the set of solutions to the linear matrix inequalities in the positive-real and bounded-real lemmas is also obtained. In addition, we obtain necessary and sufficient conditions for a system to be non-expansive that augment the bounded-real condition with new conditions relevant to uncontrollable systems.

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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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