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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Bibliographic Details
Published inInternational journal of robust and nonlinear control Vol. 33; no. 10; pp. 5484 - 5509
Main Authors Hua, Haochen, Gashi, Bujar, Zhang, Moyu
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 10.07.2023
Subjects
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
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Summary: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.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.6655