CLC number: TP273.1
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2013-12-19
Cited: 1
Clicked: 7908
Xiao-hua Wang, Juan-juan Yu, Yao Huang, Hua Wang, Zhong-hua Miao. Adaptive dynamic programming for linear impulse systems[J]. Journal of Zhejiang University Science C, 2014, 15(1): 43-50.
@article{title="Adaptive dynamic programming for linear impulse systems",
author="Xiao-hua Wang, Juan-juan Yu, Yao Huang, Hua Wang, Zhong-hua Miao",
journal="Journal of Zhejiang University Science C",
volume="15",
number="1",
pages="43-50",
year="2014",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.C1300145"
}
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%T Adaptive dynamic programming for linear impulse systems
%A Xiao-hua Wang
%A Juan-juan Yu
%A Yao Huang
%A Hua Wang
%A Zhong-hua Miao
%J Journal of Zhejiang University SCIENCE C
%V 15
%N 1
%P 43-50
%@ 1869-1951
%D 2014
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.C1300145
TY - JOUR
T1 - Adaptive dynamic programming for linear impulse systems
A1 - Xiao-hua Wang
A1 - Juan-juan Yu
A1 - Yao Huang
A1 - Hua Wang
A1 - Zhong-hua Miao
J0 - Journal of Zhejiang University Science C
VL - 15
IS - 1
SP - 43
EP - 50
%@ 1869-1951
Y1 - 2014
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.C1300145
Abstract: We investigate the optimization of linear impulse systems with the reinforcement learning based adaptive dynamic programming (ADP) method. For linear impulse systems, the optimal objective function is shown to be a quadric form of the pre-impulse states. The ADP method provides solutions that iteratively converge to the optimal objective function. If an initial guess of the pre-impulse objective function is selected as a quadratic form of the pre-impulse states, the objective function iteratively converges to the optimal one through ADP. Though direct use of the quadratic objective function of the states within the ADP method is theoretically possible, the numerical singularity problem may occur due to the matrix inversion therein when the system dimensionality increases. A neural network based ADP method can circumvent this problem. A neural network with polynomial activation functions is selected to approximate the pre-impulse objective function and trained iteratively using the ADP method to achieve optimal control. After a successful training, optimal impulse control can be derived. Simulations are presented for illustrative purposes.
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