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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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 43; no. 2; pp. 779 - 789
Main Authors: Liu, Derong, Wei, Qinglai
Format: Journal Article
Language:English
Published: United States IEEE 01.04.2013
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
ISSN:2168-2267, 2168-2275, 2168-2275
Online Access:Get full text
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Summary: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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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TSMCB.2012.2216523