Robust Adaptive Dynamic Programming and Feedback Stabilization of Nonlinear Systems
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dy...
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| Vydané v: | IEEE transaction on neural networks and learning systems Ročník 25; číslo 5; s. 882 - 893 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York, NY
IEEE
01.05.2014
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Predmet: | |
| ISSN: | 2162-237X, 2162-2388, 2162-2388 |
| On-line prístup: | Získať plný text |
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| Abstract | This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system. |
|---|---|
| AbstractList | This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system. This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system. |
| Author | Jiang, Zhong-Ping Jiang, Yu |
| Author_xml | – sequence: 1 givenname: Yu surname: Jiang fullname: Jiang, Yu email: yu.jiang@nyu.edu organization: Department of Electrical and Computer Engineering, Brooklyn, NY, USA – sequence: 2 givenname: Zhong-Ping surname: Jiang fullname: Jiang, Zhong-Ping email: zjiang@nyu.edu organization: Department of Electrical and Computer Engineering, Brooklyn, NY, USA |
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| CODEN | ITNNAL |
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| Keywords | nonlinear uncertain systems Adaptive dynamic programming (ADP) robust optimal control Methodology Non linear control Feedback regulation Control synthesis Optimization Optimal design Uncertain system Unmodeled dynamics Dynamic programming Learning algorithm Optimal control (mathematics) Single machine Adaptive dynamic programming Turbojet Reinforcement learning Jet engine Non linear system Recursive algorithm Backstepping control Robust control Optimal control Small gain theorem Control theory Artificial intelligence Output feedback Lyapunov function |
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| References | ref13 ref12 ref15 ref53 ref55 ref54 beard (ref5) 1997; 33 ref17 ref18 sutton (ref38) 1998 ref50 ref46 ref45 ref42 ref41 ref44 ref43 marino (ref27) 1995 ref8 jiang (ref11) 2012; 48 ref4 khalil (ref20) 2002 ref3 howard (ref9) 1960 bersekas (ref7) 1996 ref40 werbos (ref52) 1992 ref35 karafyllis (ref19) 2011 ref34 werbos (ref49) 1974 ref37 ref36 ref31 ref30 ref33 ref2 jiang (ref14) 2012 ref1 werbos (ref48) 1968 ref39 bellman (ref6) 1957 jiang (ref16) 1996; 32 ref24 ref23 ref26 ref25 werbos (ref51) 1991 kundur (ref22) 1994 ref28 krstic (ref21) 1995 ref29 powell (ref32) 1981 isidori (ref10) 1999; 2 watkins (ref47) 1989 |
| References_xml | – year: 1989 ident: ref47 publication-title: Learning from delayed rewards – ident: ref31 doi: 10.1109/TSMCC.2002.801727 – ident: ref26 doi: 10.1002/9781118453988 – volume: 32 start-page: 1211 year: 1996 ident: ref16 article-title: A Lyapunov formulation of the nonlinear small gain theorem for interconnected ISS systems publication-title: Automatica doi: 10.1016/0005-1098(96)00051-9 – ident: ref35 doi: 10.1109/9.28018 – year: 2002 ident: ref20 publication-title: Nonlinear Systems – ident: ref1 doi: 10.1109/TNN.2008.2000204 – ident: ref8 doi: 10.1162/089976600300015961 – year: 1995 ident: ref21 publication-title: Nonlinear and Adaptive Control Design – volume: 33 start-page: 2159 year: 1997 ident: ref5 article-title: Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation publication-title: Automatica doi: 10.1016/S0005-1098(97)00128-3 – ident: ref40 doi: 10.1137/S0363012992241430 – ident: ref45 doi: 10.1109/TAC.1965.1098193 – ident: ref41 doi: 10.1016/0167-6911(94)00016-O – ident: ref46 doi: 10.1109/MCI.2009.932261 – ident: ref37 doi: 10.1016/0167-6911(94)00050-6 – ident: ref36 doi: 10.1109/9.52307 – year: 1960 ident: ref9 publication-title: Dynamic Programming and Markov Processes – volume: 2 year: 1999 ident: ref10 publication-title: Nonlinear Control Systems doi: 10.1007/978-1-4471-0549-7 – ident: ref17 doi: 10.1109/9.557574 – volume: 48 start-page: 2699 year: 2012 ident: ref11 article-title: Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics publication-title: Automatica doi: 10.1016/j.automatica.2012.06.096 – year: 1992 ident: ref52 article-title: Approximate dynamic programming for real-time control and neural modeling publication-title: Handbook of Intelligent Control Neural Fuzzy and Adaptive Approaches – ident: ref29 doi: 10.1109/JRPROC.1961.287775 – year: 1974 ident: ref49 publication-title: Beyond Regression New Tools for Prediction and Analysis in the Behavioral Sciences – ident: ref28 doi: 10.1016/S0076-5392(08)60497-X – ident: ref24 doi: 10.1109/MCAS.2009.933854 – ident: ref55 doi: 10.1109/72.883443 – ident: ref53 doi: 10.1016/j.neunet.2009.03.012 – year: 1957 ident: ref6 publication-title: Dynamic Programming – ident: ref54 doi: 10.1016/j.automatica.2010.10.033 – year: 1981 ident: ref32 publication-title: Approximation Theory and Methods doi: 10.1017/CBO9781139171502 – ident: ref2 doi: 10.1016/j.automatica.2006.09.019 – year: 1995 ident: ref27 publication-title: Nonlinear Control Design Geometric Adaptive Robust – ident: ref39 doi: 10.1007/BF00115009 – year: 1996 ident: ref7 publication-title: Neuro-Dynamic Programming – ident: ref15 doi: 10.1016/j.ejcon.2013.05.017 – ident: ref44 doi: 10.1016/j.automatica.2008.08.017 – ident: ref3 doi: 10.1109/ICNN.1994.374604 – ident: ref12 doi: 10.1109/TNNLS.2013.2249668 – ident: ref4 doi: 10.1109/TSMC.1983.6313077 – ident: ref42 doi: 10.1016/j.automatica.2011.03.005 – ident: ref13 doi: 10.1109/CDC.2011.6160279 – ident: ref34 doi: 10.1109/TSMC.1979.4310171 – ident: ref25 doi: 10.1109/TSMCB.2010.2043839 – ident: ref30 doi: 10.1115/1.3239887 – year: 2012 ident: ref14 article-title: Robust adaptive dynamic programming publication-title: Reinforcement Learning and Approximate Dynamic Programming for Feedback Control doi: 10.1002/9781118453988.ch13 – year: 1994 ident: ref22 publication-title: Power System Stability and Control – ident: ref23 doi: 10.1002/9781118122631 – start-page: 67 year: 1991 ident: ref51 article-title: A menu of designs for reinforcement learning over time publication-title: Neural Networks for Control doi: 10.7551/mitpress/4939.003.0007 – ident: ref18 doi: 10.1007/BF01211469 – ident: ref43 doi: 10.1016/j.neunet.2009.03.008 – ident: ref33 doi: 10.1007/BF01211516 – year: 2011 ident: ref19 publication-title: Stability and Stabilization of Nonlinear Systems doi: 10.1007/978-0-85729-513-2 – year: 1998 ident: ref38 publication-title: Reinforcement Learning An Introduction – year: 1968 ident: ref48 publication-title: The Elements of Intelligence – ident: ref50 doi: 10.1109/CDC.1989.70114 |
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| SubjectTerms | Adaptative systems Adaptive dynamic programming (ADP) Applied sciences Approximation methods Artificial intelligence Closed loop systems Computer science; control theory; systems Control system synthesis Control systems Control theory Control theory. Systems Design engineering Dynamic programming Dynamical systems Exact sciences and technology Learning Learning and adaptive systems Nonlinear dynamics Nonlinear systems nonlinear uncertain systems Nonlinearity Optimal control robust optimal control Robustness Uncertainty |
| Title | Robust Adaptive Dynamic Programming and Feedback Stabilization of Nonlinear Systems |
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