State-space formulae for all stabilizing controllers that satisfy an H∞-norm bound and relations to relations to risk sensitivity

Glover, K.; Doyle, John C.

doi:10.1016/0167-6911(88)90055-2

Cited by 1,267 publications

(394 citation statements)

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“…This has resulted in a more general risk-sensitive regulator and filter. It will be interesting to extend these ideas to discrete-time setting, and explore the relation with robust controllers based on H ∞ control theory (as in [5], [6]). …”

Section: Discussionmentioning

confidence: 99%

“…The discrete-time partial observation problem was solved by Whittle in [18] (see also [19]). An important relation with robust controllers was found in [5], [6], whereas the risk-sensitive maximum principle was studied in [14], [15], [8], [10]. The optimal investment problem is particulary suitable for the application of risk-sensitive control; see for example [3], [4], [13], [7].…”

Section: [X (T)qx(t) + U (T)ru(t)]dt (2)mentioning

confidence: 99%

See 1 more Smart Citation

Generalised Risk-Sensitive Control with Full and Partial State Observation

Date

Gashi

2012

J Math Model Algor

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This paper generalises the risk-sensitive cost functional by introducing noise dependent penalties on the state and control variables. The optimal control problems for the full and partial state observation are considered. Using a change of probability measure approach, explicit closed-form solutions are found in both cases. This has resulted in a new risk-sensitive regulator and filter, which are generalisations of the well-known classical results.

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Section: Discussionmentioning

confidence: 99%

Section: [X (T)qx(t) + U (T)ru(t)]dt (2)mentioning

confidence: 99%

Generalised Risk-Sensitive Control with Full and Partial State Observation

Date

Gashi

2012

J Math Model Algor

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“…This H ∞ /LTR design problem is equivalent to a model matching which can be transformed into a standard problem with H ∞ norm minimization [8] and solved using the H ∞ control with the output feedback [9], [17], [18]. Unlike the procedure presented in method 1, the obtained unknown input observer (25) may be not of minimal order.…”

Section: Methodsmentioning

confidence: 99%

Loop transfer recovery designs with an unknown input reduced‐order observer‐based controller

Zasadzinski

Darouach

Hayar

1995

Intl J Robust & Nonlinear

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parametrizations methods for all unknown input observers are presented, the first one is based on the matrix fraction description (MFD) and the second one is developed in RH ∞ . The LTR for both minimum and non-minimum phase systems are considered. An exact recovery, based on the unknown input observer, is provided for minimum phase systems. For non-minimum phase systems, an approximate recovery is obtained by minimizing the H ∞ norm of the recovery matrix.

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“…n ¼ 2 Â 150. The H 1 controller was designed by the Glover and Doyle's method [3]. The resulting sensitivity function is shown in Fig.…”

Section: Feedback Controller Design Incorporating H 1 Controlmentioning

confidence: 99%