Discrete-Time Local Value Iteration Adaptive Dynamic Programming: Convergence Analysis
In this paper, convergence properties are established for the newly developed discrete-time local value iteration adaptive dynamic programming (ADP) algorithm. The present local iterative ADP algorithm permits an arbitrary positive semidefinite function to initialize the algorithm. Employing a state...
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| Published in | IEEE transactions on systems, man, and cybernetics. Systems Vol. 48; no. 6; pp. 875 - 891 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.06.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2168-2216 2168-2232 |
| DOI | 10.1109/TSMC.2016.2623766 |
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| Abstract | In this paper, convergence properties are established for the newly developed discrete-time local value iteration adaptive dynamic programming (ADP) algorithm. The present local iterative ADP algorithm permits an arbitrary positive semidefinite function to initialize the algorithm. Employing a state-dependent learning rate function, for the first time, the iterative value function and iterative control law can be updated in a subset of the state space instead of the whole state space, which effectively relaxes the computational burden. A new analysis method for the convergence property is developed to prove that the iterative value functions will converge to the optimum under some mild constraints. Monotonicity of the local value iteration ADP algorithm is presented, which shows that under some special conditions of the initial value function and the learning rate function, the iterative value function can monotonically converge to the optimum. Finally, three simulation examples and comparisons are given to illustrate the performance of the developed algorithm. |
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| AbstractList | In this paper, convergence properties are established for the newly developed discrete-time local value iteration adaptive dynamic programming (ADP) algorithm. The present local iterative ADP algorithm permits an arbitrary positive semidefinite function to initialize the algorithm. Employing a state-dependent learning rate function, for the first time, the iterative value function and iterative control law can be updated in a subset of the state space instead of the whole state space, which effectively relaxes the computational burden. A new analysis method for the convergence property is developed to prove that the iterative value functions will converge to the optimum under some mild constraints. Monotonicity of the local value iteration ADP algorithm is presented, which shows that under some special conditions of the initial value function and the learning rate function, the iterative value function can monotonically converge to the optimum. Finally, three simulation examples and comparisons are given to illustrate the performance of the developed algorithm. |
| Author | Wei, Qinglai Lin, Hanquan Lewis, Frank L. Liu, Derong Song, Ruizhuo |
| Author_xml | – sequence: 1 givenname: Qinglai orcidid: 0000-0001-7002-9800 surname: Wei fullname: Wei, Qinglai email: qinglai.wei@ia.ac.cn organization: The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China – sequence: 2 givenname: Frank L. surname: Lewis fullname: Lewis, Frank L. email: lewis@uta.edu organization: UTA Research Institute, The University of Texas at Arlington, Arlington, TX, USA – sequence: 3 givenname: Derong orcidid: 0000-0003-3715-4778 surname: Liu fullname: Liu, Derong email: derong@ustb.edu.cn organization: School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China – sequence: 4 givenname: Ruizhuo surname: Song fullname: Song, Ruizhuo email: ruishuosong@ustb.edu.cn organization: School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China – sequence: 5 givenname: Hanquan surname: Lin fullname: Lin, Hanquan email: hanquan.lin@ia.ac.cn organization: The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China |
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| SubjectTerms | Adaptive algorithms Adaptive critic designs adaptive dynamic programming (ADP) Aerospace electronics Algorithms approximate dynamic programming Approximation algorithms Computer simulation Control theory Convergence Dynamic programming Iterative algorithms Iterative methods local iteration Machine learning neural networks neuro-dynamic programming Nonlinear systems Optimal control |
| Title | Discrete-Time Local Value Iteration Adaptive Dynamic Programming: Convergence Analysis |
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