Minimax LQG control

Ian Petersen

International Journal of Applied Mathematics and Computer Science (2006)

  • Volume: 16, Issue: 3, page 309-323
  • ISSN: 1641-876X

Abstract

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This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under consideration is further motivated by analysing the basic properties of relative entropy. The paper then presents a solution to a worst case control system performance problem which can be generalized to the minimax LQG problem. The solution to this minimax LQG control problem is found to be closely connected to the problem of risk-sensitive optimal control.

How to cite

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Petersen, Ian. "Minimax LQG control." International Journal of Applied Mathematics and Computer Science 16.3 (2006): 309-323. <http://eudml.org/doc/207795>.

@article{Petersen2006,
abstract = {This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under consideration is further motivated by analysing the basic properties of relative entropy. The paper then presents a solution to a worst case control system performance problem which can be generalized to the minimax LQG problem. The solution to this minimax LQG control problem is found to be closely connected to the problem of risk-sensitive optimal control.},
author = {Petersen, Ian},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {robust control; risk-sensitive control; minimax control; stochastic uncertain system; LQGcontrol; output-feedback control; LQG control},
language = {eng},
number = {3},
pages = {309-323},
title = {Minimax LQG control},
url = {http://eudml.org/doc/207795},
volume = {16},
year = {2006},
}

TY - JOUR
AU - Petersen, Ian
TI - Minimax LQG control
JO - International Journal of Applied Mathematics and Computer Science
PY - 2006
VL - 16
IS - 3
SP - 309
EP - 323
AB - This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under consideration is further motivated by analysing the basic properties of relative entropy. The paper then presents a solution to a worst case control system performance problem which can be generalized to the minimax LQG problem. The solution to this minimax LQG control problem is found to be closely connected to the problem of risk-sensitive optimal control.
LA - eng
KW - robust control; risk-sensitive control; minimax control; stochastic uncertain system; LQGcontrol; output-feedback control; LQG control
UR - http://eudml.org/doc/207795
ER -

References

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