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Laguerre Bases for Youla-Parametrized Optimal-Controller Design: Numerical Issues and Solutions

Kjellqvist, Olle LU orcid (2018)
Abstract
This thesis concerns the evaluation of cost functionals on H2 when designing optimal controllers using finite Youla parameterizations and convex optimization. We propose to compute inner products of stable, strictly proper systems via solving Sylvester equations. The properties of different state space realizations of Laguerre filters, when performing Ritz expansions of the optimal controller are discussed, and a closed form expression of the output orthogonal realization is presented. An algorithm to exploit Toeplitz substructure when solving Lyapunov equations is discussed, and a method to extend SISO results to MIMO systems using the vectorization operator is proposed. Finally the methods are evaluated on example systems from the... (More)
This thesis concerns the evaluation of cost functionals on H2 when designing optimal controllers using finite Youla parameterizations and convex optimization. We propose to compute inner products of stable, strictly proper systems via solving Sylvester equations. The properties of different state space realizations of Laguerre filters, when performing Ritz expansions of the optimal controller are discussed, and a closed form expression of the output orthogonal realization is presented. An algorithm to exploit Toeplitz substructure when solving Lyapunov equations is discussed, and a method to extend SISO results to MIMO systems using the vectorization operator is proposed. Finally the methods are evaluated on example systems from the industry, where it is shown that properly selecting the cutoff frequency of the filters is an important problem that should be discussed when Laguerre bases are used to parametrize the optimal controller. (Less)
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supervisor
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Thesis
publication status
published
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pages
69 pages
language
English
LU publication?
yes
id
21ea013c-a332-447b-a607-ebfdf3229940
alternative location
https://lup.lub.lu.se/student-papers/search/publication/8953453
date added to LUP
2022-07-15 10:46:36
date last changed
2022-08-18 09:34:54
@misc{21ea013c-a332-447b-a607-ebfdf3229940,
  abstract     = {{This thesis concerns the evaluation of cost functionals on H2 when designing optimal controllers using finite Youla parameterizations and convex optimization. We propose to compute inner products of stable, strictly proper systems via solving Sylvester equations. The properties of different state space realizations of Laguerre filters, when performing Ritz expansions of the optimal controller are discussed, and a closed form expression of the output orthogonal realization is presented. An algorithm to exploit Toeplitz substructure when solving Lyapunov equations is discussed, and a method to extend SISO results to MIMO systems using the vectorization operator is proposed. Finally the methods are evaluated on example systems from the industry, where it is shown that properly selecting the cutoff frequency of the filters is an important problem that should be discussed when Laguerre bases are used to parametrize the optimal controller.}},
  author       = {{Kjellqvist, Olle}},
  language     = {{eng}},
  month        = {{06}},
  title        = {{Laguerre Bases for Youla-Parametrized Optimal-Controller Design: Numerical Issues and Solutions}},
  url          = {{https://lup.lub.lu.se/student-papers/search/publication/8953453}},
  year         = {{2018}},
}