Robust control of set-valued discrete-time dynamical systems
This paper presents results obtained for the control of set-valued discrete-time dynamical systems. Such systems model nonlinear systems subject to persistent bounded noise. A robust control problem for such systems is introduced. The problem is formulated as a dynamic game, wherein the controller p...
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| Published in | IEEE transactions on automatic control Vol. 43; no. 1; pp. 61 - 75 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.01.1998
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 |
| DOI | 10.1109/9.654887 |
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| Abstract | This paper presents results obtained for the control of set-valued discrete-time dynamical systems. Such systems model nonlinear systems subject to persistent bounded noise. A robust control problem for such systems is introduced. The problem is formulated as a dynamic game, wherein the controller plays against the set-valued system. Both necessary and sufficient conditions in terms of (stationary) dynamic programming equalities are presented. The output feedback problem is solved using the concept of an information state, where a decoupling between estimation and control is obtained. The methods yield a conceptual approach for constructing controlled-invariant sets and stabilizing controllers for uncertain nonlinear systems. |
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| AbstractList | This paper presents results obtained for the control of set-valued discrete-time dynamical systems. Such systems model nonlinear systems subject to persistent bounded noise. A robust control problem for such systems is introduced. The problem is formulated as a dynamic game, wherein the controller plays against the set-valued system. Both necessary and sufficient conditions in terms of (stationary) dynamic programming equalities are presented. The output feedback problem is solved using the concept of an information state, where a decoupling between estimation and control is obtained. The methods yield a conceptual approach for constructing controlled-invariant sets and stabilizing controllers for uncertain nonlinear systems. (Author) This paper presents results obtained for the control of set-valued discrete-time dynamical systems. Such systems model nonlinear systems subject to persistent bounded noise. A robust control problem for such systems is introduced. The problem is formulated as a dynamic game, wherein the controller plays against the set-valued system. Both necessary and sufficient conditions in terms of (stationary) dynamic programming equalities are presented. The output feedback problem is solved using the concept of an information state, where a decoupling between estimation and control is obtained. The methods yield a conceptual approach for constructing controlled-invariant sets and stabilizing controllers for uncertain nonlinear systems This paper presents results obtained for the control of set-valued discrete-time dynamical systems. Such systems model nonlinear systems subject to persistent bounded noise. A robust control problem for such systems is introduced. The problem is formulated as a dynamic game, wherein the controller plays against the set-valued system. Both necessary and sufficient conditions in terms of (stationary) dynamic programming equalities are presented. The output feedback problem is solved using the concept of an information state, where a decoupling between estimation and control is obtained. The methods yield a conceptual approach for constructing controlled-invariant sets and stabilizing controllers for uncertain nonlinear systems. |
| Author | Baras, J.S. Patel, N.S. |
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| Cites_doi | 10.1007/BFb0087685 10.1109/CDC.1995.480546 10.1109/CDC.1993.325166 10.1109/TAC.1987.1104603 10.1109/CDC.1994.411621 10.1007/BF01211560 10.1137/0326069 10.1137/0326070 10.1109/CDC.1989.70671 10.1016/0005-1098(83)90007-9 10.1002/rnc.4590010304 10.1109/9.388678 10.1016/0005-1098(86)90045-2 10.1109/9.256331 10.23919/ACC.1991.4791667 10.1109/CDC.1994.411688 10.1007/978-94-015-7793-9 10.1109/9.272351 10.2307/1426972 |
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| Keywords | Robust control Dynamic game Control synthesis Certainty equivalence principle Discrete system Dynamic programming Non linear system Output feedback Convergence |
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| References_xml | – year: 1977 ident: ref25 publication-title: Convex Analysis and Measurable Multifunctions doi: 10.1007/BFb0087685 – start-page: 829 year: 1995 ident: ref12 article-title: attenuation of persistent ${l}_{\infty}$-bounded disturbances for nonlinear systems publication-title: Proc 34th IEEE Conf Decision Contr – ident: ref15 doi: 10.1109/CDC.1995.480546 – year: 1984 ident: ref21 publication-title: Applied Nonlinear Analysis – ident: ref17 doi: 10.1109/CDC.1993.325166 – start-page: 3265 year: 1992 ident: ref18 article-title: dissipation inequalities in nonlinear $h_{\infty}$-control publication-title: Proc 31st IEEE Conf Decision Contr – volume: 32 start-page: 314 year: 1987 ident: ref6 article-title: $l^1$-optimal feedback controllers for mimo discrete-time systems publication-title: IEEE Transactions on Automatic Control doi: 10.1109/TAC.1987.1104603 – ident: ref24 doi: 10.1109/CDC.1994.411621 – volume: 5 start-page: 233 year: 1992 ident: ref16 article-title: nonlinear $h_{\infty}$ control theory for stable plants publication-title: Math Contr Sig Syst doi: 10.1007/BF01211560 – ident: ref3 doi: 10.1137/0326069 – ident: ref2 doi: 10.1137/0326070 – ident: ref9 doi: 10.1109/CDC.1989.70671 – ident: ref5 doi: 10.1016/0005-1098(83)90007-9 – year: 1990 ident: ref22 publication-title: Set-Valued Analysis – volume: 1 start-page: 171 year: 1991 ident: ref19 article-title: a first principles solution to the nonsingular ${h}_{\infty}$ control problem publication-title: Int J Robust Nonlinear Contr doi: 10.1002/rnc.4590010304 – year: 1991 ident: ref13 publication-title: Viability Theory – volume: 40 start-page: 1007 year: 1995 ident: ref14 article-title: robust $h_{\infty}$ output feedback control for nonlinear systems publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.388678 – ident: ref4 doi: 10.1016/0005-1098(86)90045-2 – volume: 37 start-page: 770 year: 1992 ident: ref20 article-title: $l_2$ gain analysis of nonlinear systems and nonlinear state feedback $h_{\infty}$ control publication-title: IEEE Transactions on Automatic Control doi: 10.1109/9.256331 – start-page: 40 year: 1994 ident: ref7 article-title: construction of nonlinear feedback for $l_1$-optimal control publication-title: Proc 33rd IEEE Conf Decision Contr – year: 1994 ident: ref1 publication-title: New Tools for Robustness of Linear Systems – start-page: 1679 year: 1991 ident: ref8 article-title: asymptotic stability of m-switched systems using lyapunov-like functions publication-title: 1991 American Control Conference ACC doi: 10.23919/ACC.1991.4791667 – ident: ref10 doi: 10.1109/CDC.1994.411688 – year: 1988 ident: ref11 publication-title: Differential Equations with Discontinuous Righthand Sides doi: 10.1007/978-94-015-7793-9 – ident: ref23 doi: 10.1109/9.272351 – ident: ref26 doi: 10.2307/1426972 |
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| SubjectTerms | Applied sciences Computer science; control theory; systems Control system synthesis Control systems Control theory. Systems Exact sciences and technology Linear systems Nonlinear control systems Nonlinear dynamical systems Nonlinear systems Output feedback Robust control Shape control State estimation Sufficient conditions |
| Title | Robust control of set-valued discrete-time dynamical systems |
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