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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| Veröffentlicht in: | International journal of robust and nonlinear control Jg. 33; H. 10; S. 5484 - 5509 |
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| Sprache: | Englisch |
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Bognor Regis
Wiley Subscription Services, Inc
10.07.2023
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| ISSN: | 1049-8923, 1099-1239 |
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| Abstract | 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. |
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| AbstractList | 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. 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. We introduce a risk‐sensitive generalization of the mixed 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. |
| Author | Zhang, Moyu Hua, Haochen Gashi, Bujar |
| Author_xml | – sequence: 1 givenname: Haochen orcidid: 0000-0002-3341-2947 surname: Hua fullname: Hua, Haochen email: Huahc16@tsinghua.org.cn organization: Hohai University – sequence: 2 givenname: Bujar surname: Gashi fullname: Gashi, Bujar organization: University of Liverpool – sequence: 3 givenname: Moyu surname: Zhang fullname: Zhang, Moyu organization: Guangdong Yuecai Investment Holdings |
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We introduce a risk‐sensitive generalization of the mixed H2/H∞$$ {H}_2/{H}_{\infty } $$ control problem for linear stochastic systems with additive... We introduce a risk‐sensitive generalization of the mixed control problem for linear stochastic systems with additive noise. Two criteria of... 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... |
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| SubjectTerms | 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 |
| Title | Robust risk‐sensitive control |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Frnc.6655 https://www.proquest.com/docview/2821538758 |
| Volume | 33 |
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