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Inverse Quadratic Optimal Control for Discrete-Time Linear Systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-3905-0633
Department of Information Technology, Division of Systems and Control, Uppsala University.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0003-0177-1993
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper, we consider the inverse optimal control problem for discrete-time Linear Quadratic Regulators (LQRs), over finite-time horizons. Given observations of the optimal trajectories, or optimal control inputs, to a linear time-invariant system, the goal is to infer the parameters that define the quadratic cost function. The well-posedness of the inverse optimal control problem is first justied. In the noiseless case, when these observations are exact, we analyze the identiability of the problem and provide sufficient conditions for uniqueness of the solution. In the noisy case, when the observations are corrupted by additive zero-mean noise, we formulate the problem as an optimization problem and prove that the solution to this problem is statistically consistent. The performance of the proposed method is illustrated through numerical examples.

Keywords [en]
Inverse optimal control, Linear Quadratic Regulator
National Category
Control Engineering Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-241428OAI: oai:DiVA.org:kth-241428DiVA, id: diva2:1280938
Note

QC 20190121

Available from: 2019-01-21 Created: 2019-01-21 Last updated: 2019-01-21Bibliographically approved

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fulltext(474 kB)5 downloads
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Zhang, HanHu, Xiaoming

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf