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Linear Quadratic Control under Quadratic Constraints

Rantzer, Anders LU orcid and van der Geest, Robert (1997) 4th European Control Conference, 1997 p.3363-3368
Abstract
The linear quadratic optimal control problem under quadratic constraints is an optimization problem over a generally non-convex set. Yakubovich [8] and Megretski [4] have studied this problem, and they show how it may be translated into a two-stage, convex optimization problem. In this paper we study the linear quadratic control problem under quadratic constraints for generalized first-order systems. As in the state-space case the linear quadratic control problem without quadratic constraints may be solved in terms of a linear matrix inequality. Subsequently, we use the results from [8] to derive a linear matrix inequality characterizing the linear quadratic optimal behaviour under quadratic constraints.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
1997 European Control Conference (ECC)
pages
3363 - 3368
conference name
4th European Control Conference, 1997
conference location
Brussels, Belgium
conference dates
1997-07-01 - 1997-07-04
external identifiers
  • scopus:84949086512
ISBN
978-3-9524269-0-6
language
English
LU publication?
yes
id
903d686f-9fca-47e1-a0e8-a4bf75a4da76 (old id 8517032)
date added to LUP
2016-04-04 13:26:43
date last changed
2023-04-09 03:18:58
@inproceedings{903d686f-9fca-47e1-a0e8-a4bf75a4da76,
  abstract     = {{The linear quadratic optimal control problem under quadratic constraints is an optimization problem over a generally non-convex set. Yakubovich [8] and Megretski [4] have studied this problem, and they show how it may be translated into a two-stage, convex optimization problem. In this paper we study the linear quadratic control problem under quadratic constraints for generalized first-order systems. As in the state-space case the linear quadratic control problem without quadratic constraints may be solved in terms of a linear matrix inequality. Subsequently, we use the results from [8] to derive a linear matrix inequality characterizing the linear quadratic optimal behaviour under quadratic constraints.}},
  author       = {{Rantzer, Anders and van der Geest, Robert}},
  booktitle    = {{1997 European Control Conference (ECC)}},
  isbn         = {{978-3-9524269-0-6}},
  language     = {{eng}},
  pages        = {{3363--3368}},
  title        = {{Linear Quadratic Control under Quadratic Constraints}},
  year         = {{1997}},
}