Finite-Approximation-Error-Based Optimal Control Approach for Discrete-Time Nonlinear Systems
In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite-horizon discrete-time nonlinear systems with finite approximation errors. The idea is to use an iterative ADP algorithm to obtain the iterative control law that mak...
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| Vydáno v: | IEEE transactions on cybernetics Ročník 43; číslo 2; s. 779 - 789 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
United States
IEEE
01.04.2013
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Témata: | |
| ISSN: | 2168-2267, 2168-2275, 2168-2275 |
| On-line přístup: | Získat plný text |
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| Abstract | In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite-horizon discrete-time nonlinear systems with finite approximation errors. The idea is to use an iterative ADP algorithm to obtain the iterative control law that makes the iterative performance index function reach the optimum. When the iterative control law and the iterative performance index function in each iteration cannot be accurately obtained, the convergence conditions of the iterative ADP algorithm are obtained. When convergence conditions are satisfied, it is shown that the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some mild assumptions. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method. |
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| AbstractList | In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite-horizon discrete-time nonlinear systems with finite approximation errors. The idea is to use an iterative ADP algorithm to obtain the iterative control law that makes the iterative performance index function reach the optimum. When the iterative control law and the iterative performance index function in each iteration cannot be accurately obtained, the convergence conditions of the iterative ADP algorithm are obtained. When convergence conditions are satisfied, it is shown that the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some mild assumptions. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method. In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite-horizon discrete-time nonlinear systems with finite approximation errors. The idea is to use an iterative ADP algorithm to obtain the iterative control law that makes the iterative performance index function reach the optimum. When the iterative control law and the iterative performance index function in each iteration cannot be accurately obtained, the convergence conditions of the iterative ADP algorithm are obtained. When convergence conditions are satisfied, it is shown that the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some mild assumptions. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite-horizon discrete-time nonlinear systems with finite approximation errors. The idea is to use an iterative ADP algorithm to obtain the iterative control law that makes the iterative performance index function reach the optimum. When the iterative control law and the iterative performance index function in each iteration cannot be accurately obtained, the convergence conditions of the iterative ADP algorithm are obtained. When convergence conditions are satisfied, it is shown that the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some mild assumptions. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method. |
| Author | Wei, Qinglai Liu, Derong |
| Author_xml | – sequence: 1 givenname: Derong surname: Liu fullname: Liu, Derong email: derong.liu@ia.ac.cn organization: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China – sequence: 2 givenname: Qinglai surname: Wei fullname: Wei, Qinglai email: qinglai.wei@ia.ac.cn organization: State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/23070311$$D View this record in MEDLINE/PubMed |
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| CODEN | ITCEB8 |
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| SubjectTerms | Adaptive dynamic programming (ADP) Algorithms approximate dynamic programming Approximation algorithms Approximation error Convergence Dynamic programming Dynamical systems finite approximation errors Heuristic algorithms Iterative algorithms Iterative methods Mathematical analysis Mathematical models Neural networks Nonlinear dynamics Nonlinear systems Optimal control Optimization Performance analysis Performance indices Studies |
| Title | Finite-Approximation-Error-Based Optimal Control Approach for Discrete-Time Nonlinear Systems |
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