Robust risk‐sensitive control

Summary We introduce a risk‐sensitive generalization of the mixed H2/H∞$$ {H}_2/{H}_{\infty } $$ control problem for linear stochastic systems with additive noise. Two criteria of exponential‐quadratic form are used to generalise the usual quadratic criteria. The solutions are found in a linear stat...

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Vydané v:	International journal of robust and nonlinear control Ročník 33; číslo 10; s. 5484 - 5509
Hlavní autori:	Hua, Haochen, Gashi, Bujar, Zhang, Moyu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Bognor Regis Wiley Subscription Services, Inc 10.07.2023
Predmet:	Criteria Differential equations H-infinity control Mathematical analysis Quadratic forms Risk management risk‐sensitive control Robust control robust portfolio control stochastic mixed H2/H∞$$ {H}_2/{H}_{\infty } $$ control Stochastic systems
ISSN:	1049-8923, 1099-1239
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Shrnutí:	Summary We introduce a risk‐sensitive generalization of the mixed H2/H∞$$ {H}_2/{H}_{\infty } $$ control problem for linear stochastic systems with additive noise. Two criteria of exponential‐quadratic form are used to generalise the usual quadratic criteria. The solutions are found in a linear state‐feedback form for both the finite and the infinite horizon formulations in terms of coupled Riccati differential and algebraic equations. A change of measures for both criteria and completion of squares method is used to derive the solutions, and explicit sufficient conditions for the admissibility of controls are derived. An application to the problem of robust portfolio control in a market with random interest rate subject to a disturbance is also given.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1049-8923 1099-1239
DOI:	10.1002/rnc.6655