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Closed-form H-infinity optimal control for a class of infinite-dimensional systems

Bergeling, Carolina LU ; Morris, Kirsten A. and Rantzer, Anders LU (2020) In Automatica 117.
Abstract

H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is needed to obtain the optimal solution. Moreover, the optimal performance for both the state feedback and state estimation problems are explicitly calculated. This is shown to be useful for problems of H-infinity optimal actuator and sensor location. Furthermore, the results can be used in testing and bench-marking of general purpose... (More)

H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is needed to obtain the optimal solution. Moreover, the optimal performance for both the state feedback and state estimation problems are explicitly calculated. This is shown to be useful for problems of H-infinity optimal actuator and sensor location. Furthermore, the results can be used in testing and bench-marking of general purpose algorithms for H-infinity synthesis. The results also apply to finite-dimensional systems.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Distributed-parameter systems, H-infinity control, Linear systems, Optimal control, Optimal estimation
in
Automatica
volume
117
article number
108916
publisher
Pergamon
external identifiers
  • scopus:85082447140
ISSN
0005-1098
DOI
10.1016/j.automatica.2020.108916
language
English
LU publication?
yes
id
99b7d099-b500-4d1f-aed1-58ecad228d41
date added to LUP
2020-04-15 16:40:30
date last changed
2020-12-29 03:39:48
@article{99b7d099-b500-4d1f-aed1-58ecad228d41,
  abstract     = {<p>H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is needed to obtain the optimal solution. Moreover, the optimal performance for both the state feedback and state estimation problems are explicitly calculated. This is shown to be useful for problems of H-infinity optimal actuator and sensor location. Furthermore, the results can be used in testing and bench-marking of general purpose algorithms for H-infinity synthesis. The results also apply to finite-dimensional systems.</p>},
  author       = {Bergeling, Carolina and Morris, Kirsten A. and Rantzer, Anders},
  issn         = {0005-1098},
  language     = {eng},
  publisher    = {Pergamon},
  series       = {Automatica},
  title        = {Closed-form H-infinity optimal control for a class of infinite-dimensional systems},
  url          = {http://dx.doi.org/10.1016/j.automatica.2020.108916},
  doi          = {10.1016/j.automatica.2020.108916},
  volume       = {117},
  year         = {2020},
}