Neural-Network-Based Optimal Control for a Class of Unknown Discrete-Time Nonlinear Systems Using Globalized Dual Heuristic Programming
In this paper, a neuro-optimal control scheme for a class of unknown discrete-time nonlinear systems with discount factor in the cost function is developed. The iterative adaptive dynamic programming algorithm using globalized dual heuristic programming technique is introduced to obtain the optimal...
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| Veröffentlicht in: | IEEE transactions on automation science and engineering Jg. 9; H. 3; S. 628 - 634 |
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| Hauptverfasser: | , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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Piscataway, NJ
IEEE
01.07.2012
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1545-5955, 1558-3783 |
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| Abstract | In this paper, a neuro-optimal control scheme for a class of unknown discrete-time nonlinear systems with discount factor in the cost function is developed. The iterative adaptive dynamic programming algorithm using globalized dual heuristic programming technique is introduced to obtain the optimal controller with convergence analysis in terms of cost function and control law. In order to carry out the iterative algorithm, a neural network is constructed first to identify the unknown controlled system. Then, based on the learned system model, two other neural networks are employed as parametric structures to facilitate the implementation of the iterative algorithm, which aims at approximating at each iteration the cost function and its derivatives and the control law, respectively. Finally, a simulation example is provided to verify the effectiveness of the proposed optimal control approach. Note to Practitioners-The increasing complexity of the real-world industry processes inevitably leads to the occurrence of nonlinearity and high dimensions, and their mathematical models are often difficult to build. How to design the optimal controller for nonlinear systems without the requirement of knowing the explicit model has become one of the main foci of control practitioners. However, this problem cannot be handled by only relying on the traditional dynamic programming technique because of the "curse of dimensionality". To make things worse, the backward direction of solving process of dynamic programming precludes its wide application in practice. Therefore, in this paper, the iterative adaptive dynamic programming algorithm is proposed to deal with the optimal control problem for a class of unknown nonlinear systems forward-in-time. Moreover, the detailed implementation of the iterative ADP algorithm through the globalized dual heuristic programming technique is also presented by using neural networks. Finally, the effectiveness of the control strategy is illustrated via simulation study. |
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| AbstractList | In this paper, a neuro-optimal control scheme for a class of unknown discrete-time nonlinear systems with discount factor in the cost function is developed. The iterative adaptive dynamic programming algorithm using globalized dual heuristic programming technique is introduced to obtain the optimal controller with convergence analysis in terms of cost function and control law. In order to carry out the iterative algorithm, a neural network is constructed first to identify the unknown controlled system. Then, based on the learned system model, two other neural networks are employed as parametric structures to facilitate the implementation of the iterative algorithm, which aims at approximating at each iteration the cost function and its derivatives and the control law, respectively. Finally, a simulation example is provided to verify the effectiveness of the proposed optimal control approach. [PUBLICATION ABSTRACT] In this paper, a neuro-optimal control scheme for a class of unknown discrete-time nonlinear systems with discount factor in the cost function is developed. The iterative adaptive dynamic programming algorithm using globalized dual heuristic programming technique is introduced to obtain the optimal controller with convergence analysis in terms of cost function and control law. In order to carry out the iterative algorithm, a neural network is constructed first to identify the unknown controlled system. Then, based on the learned system model, two other neural networks are employed as parametric structures to facilitate the implementation of the iterative algorithm, which aims at approximating at each iteration the cost function and its derivatives and the control law, respectively. Finally, a simulation example is provided to verify the effectiveness of the proposed optimal control approach. Note to Practitioners-The increasing complexity of the real-world industry processes inevitably leads to the occurrence of nonlinearity and high dimensions, and their mathematical models are often difficult to build. How to design the optimal controller for nonlinear systems without the requirement of knowing the explicit model has become one of the main foci of control practitioners. However, this problem cannot be handled by only relying on the traditional dynamic programming technique because of the "curse of dimensionality". To make things worse, the backward direction of solving process of dynamic programming precludes its wide application in practice. Therefore, in this paper, the iterative adaptive dynamic programming algorithm is proposed to deal with the optimal control problem for a class of unknown nonlinear systems forward-in-time. Moreover, the detailed implementation of the iterative ADP algorithm through the globalized dual heuristic programming technique is also presented by using neural networks. Finally, the effectiveness of the control strategy is illustrated via simulation study. |
| Author | Ding Wang Ning Jin Derong Liu Qinglai Wei Dongbin Zhao |
| Author_xml | – sequence: 1 givenname: Derong surname: Liu fullname: Liu, Derong – sequence: 2 givenname: Ding surname: Wang fullname: Wang, Ding – sequence: 3 givenname: Dongbin surname: Zhao fullname: Zhao, Dongbin – sequence: 4 givenname: Qinglai surname: Wei fullname: Wei, Qinglai – sequence: 5 givenname: Ning surname: Jin fullname: Jin, Ning |
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| Keywords | Adaptive algorithm Control program neural networks Non linear control Iterative method Heuristic programming Efficiency Cost function Dynamic programming Optimal control (mathematics) Generic programming Numerical convergence Intelligent control approximate dynamic programming Adaptive dynamic programming globalized dual heuristic programming Neural network Non linear system Cost control Neurocontrollers Optimal control Discrete time Distributed control Function derivative Derivative control |
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| References_xml | – volume: 22 start-page: 1133 year: 2011 ident: ref7 article-title: Adaptive learning and control for MIMO system based on adaptive dynamic programming publication-title: IEEE Trans Neural Netw doi: 10.1109/TNN.2011.2147797 – year: 1996 ident: ref11 publication-title: Neuro-Dynamic Programming – year: 1957 ident: ref1 publication-title: Dynamic Programming – ident: ref23 doi: 10.1109/TNN.2009.2027233 – ident: ref26 doi: 10.1016/j.neucom.2011.03.058 – ident: ref20 doi: 10.1109/TASE.2005.844122 – year: 2006 ident: ref14 publication-title: Neural Network Control of Nonlinear Discrete-time Systems – ident: ref16 doi: 10.1109/TASE.2006.879915 – ident: ref17 doi: 10.1109/ADPRL.2011.5967357 – ident: ref28 doi: 10.1109/TASE.2011.2160537 – ident: ref10 doi: 10.1109/TSMCB.2008.926614 – ident: ref12 doi: 10.1109/72.914523 – year: 1992 ident: ref4 publication-title: Handbook of Intelligent Control Neural Fuzzy and Adaptive Approaches – ident: ref27 doi: 10.1016/j.automatica.2010.02.018 – ident: ref9 doi: 10.1002/9780470182963 – ident: ref25 doi: 10.1016/j.neunet.2009.06.014 – ident: ref6 doi: 10.1109/MCAS.2009.933854 – ident: ref5 doi: 10.1109/MCI.2009.932261 – ident: ref13 doi: 10.1109/72.623201 – ident: ref19 doi: 10.1109/TNN.2002.1000146 – ident: ref8 doi: 10.1109/TNN.2010.2076370 – ident: ref18 doi: 10.1109/TNN.2005.853408 – ident: ref3 doi: 10.1109/ADPRL.2007.368190 – ident: ref22 doi: 10.1109/TSMCB.2008.926599 – ident: ref24 doi: 10.1016/j.neunet.2009.03.008 – ident: ref2 doi: 10.1016/j.neunet.2009.03.012 – volume: 41 start-page: 779 year: 2005 ident: ref21 article-title: Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach publication-title: Automatica doi: 10.1016/j.automatica.2004.11.034 – ident: ref15 doi: 10.1109/TSMCB.2006.883869 |
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| SubjectTerms | Adaptive dynamic programming Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences approximate dynamic programming Computer science; control theory; systems Computer systems and distributed systems. User interface Control system synthesis Control theory. Systems Controllers Convergence Discrete time systems Dynamic programming Exact sciences and technology globalized dual heuristic programming Heuristic Intelligent control Neural networks Optimal control Software Theoretical computing |
| Title | Neural-Network-Based Optimal Control for a Class of Unknown Discrete-Time Nonlinear Systems Using Globalized Dual Heuristic Programming |
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