Model-Free Dual Heuristic Dynamic Programming

Model-based dual heuristic dynamic programming (MB-DHP) is a popular approach in approximating optimal solutions in control problems. Yet, it usually requires offline training for the model network, and thus resulting in extra computational cost. In this brief, we propose a model-free DHP (MF-DHP) d...

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Published in:	IEEE transaction on neural networks and learning systems Vol. 26; no. 8; pp. 1834 - 1839
Main Authors:	Zhen Ni, Haibo He, Xiangnan Zhong, Prokhorov, Danil V.
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.08.2015
Subjects:	Action-dependent dual heuristic dynamic programming (DHP) adaptive critic designs (ACDs) adaptive dynamic programming (ADP) Approximation methods Computational modeling Convergence Dynamic programming Learning systems Linear programming Mathematical model online learning reinforcement learning adaptive critic designs (ACDs) Action-dependent dual heuristic dynamic programming (DHP) adaptive dynamic programming (ADP) online learning reinforcement learning
ISSN:	2162-237X, 2162-2388, 2162-2388
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Abstract	Model-based dual heuristic dynamic programming (MB-DHP) is a popular approach in approximating optimal solutions in control problems. Yet, it usually requires offline training for the model network, and thus resulting in extra computational cost. In this brief, we propose a model-free DHP (MF-DHP) design based on finite-difference technique. In particular, we adopt multilayer perceptron with one hidden layer for both the action and the critic networks design, and use delayed objective functions to train both the action and the critic networks online over time. We test both the MF-DHP and MB-DHP approaches with a discrete time example and a continuous time example under the same parameter settings. Our simulation results demonstrate that the MF-DHP approach can obtain a control performance competitive with that of the traditional MB-DHP approach while requiring less computational resources.
AbstractList	Model-based dual heuristic dynamic programming (MB-DHP) is a popular approach in approximating optimal solutions in control problems. Yet, it usually requires offline training for the model network, and thus resulting in extra computational cost. In this brief, we propose a model-free DHP (MF-DHP) design based on finite-difference technique. In particular, we adopt multilayer perceptron with one hidden layer for both the action and the critic networks design, and use delayed objective functions to train both the action and the critic networks online over time. We test both the MF-DHP and MB-DHP approaches with a discrete time example and a continuous time example under the same parameter settings. Our simulation results demonstrate that the MF-DHP approach can obtain a control performance competitive with that of the traditional MB-DHP approach while requiring less computational resources. Model-based dual heuristic dynamic programming (MB-DHP) is a popular approach in approximating optimal solutions in control problems. Yet, it usually requires offline training for the model network, and thus resulting in extra computational cost. In this brief, we propose a model-free DHP (MF-DHP) design based on finite-difference technique. In particular, we adopt multilayer perceptron with one hidden layer for both the action and the critic networks design, and use delayed objective functions to train both the action and the critic networks online over time. We test both the MF-DHP and MB-DHP approaches with a discrete time example and a continuous time example under the same parameter settings. Our simulation results demonstrate that the MF-DHP approach can obtain a control performance competitive with that of the traditional MB-DHP approach while requiring less computational resources.Model-based dual heuristic dynamic programming (MB-DHP) is a popular approach in approximating optimal solutions in control problems. Yet, it usually requires offline training for the model network, and thus resulting in extra computational cost. In this brief, we propose a model-free DHP (MF-DHP) design based on finite-difference technique. In particular, we adopt multilayer perceptron with one hidden layer for both the action and the critic networks design, and use delayed objective functions to train both the action and the critic networks online over time. We test both the MF-DHP and MB-DHP approaches with a discrete time example and a continuous time example under the same parameter settings. Our simulation results demonstrate that the MF-DHP approach can obtain a control performance competitive with that of the traditional MB-DHP approach while requiring less computational resources.
Author	Haibo He Zhen Ni Xiangnan Zhong Prokhorov, Danil V.
Author_xml	– sequence: 1 surname: Zhen Ni fullname: Zhen Ni email: ni@ele.uri.edu organization: Dept. of Electr., Univ. of Rhode Island, Kingston, RI, USA – sequence: 2 surname: Haibo He fullname: Haibo He email: he@ele.uri.edu organization: Dept. of Electr., Univ. of Rhode Island, Kingston, RI, USA – sequence: 3 surname: Xiangnan Zhong fullname: Xiangnan Zhong email: xzhong@ele.uri.edu organization: Dept. of Electr., Univ. of Rhode Island, Kingston, RI, USA – sequence: 4 givenname: Danil V. surname: Prokhorov fullname: Prokhorov, Danil V. email: dvprokhorov@gmail.com organization: Toyota Tech. Center, Toyota Res. Inst. of North America, Ann Arbor, MI, USA
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References	ref13 ref12 ref15 ref14 ref53 ref11 ref10 ref17 liu (ref24) 2014; 25 ref16 bertsekas (ref1) 1995 ref51 ref50 liu (ref18) 2013; 43 ni (ref33) 2013; 24 ref45 ref48 ref47 ref42 ref41 ref44 ref43 ref49 li (ref46) 1989 ref8 ref7 ref9 ref3 ref6 ref5 ref40 ref35 ref34 ref37 ref36 ref31 ref30 ref32 ref2 ref38 ge (ref52) 2008; 19 liu (ref22) 2014; 25 ref23 ref26 ref25 ref20 xu (ref19) 2014; 25 ref21 ni (ref39) 2015 ref28 ref27 ref29 lewis (ref4) 2013
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SubjectTerms	Action-dependent dual heuristic dynamic programming (DHP) adaptive critic designs (ACDs) adaptive dynamic programming (ADP) Approximation methods Computational modeling Convergence Dynamic programming Learning systems Linear programming Mathematical model online learning reinforcement learning
Title	Model-Free Dual Heuristic Dynamic Programming
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