Neural network optimal control for nonlinear system based on zero-sum differential game

Fu Xingjian; Li Zizheng

Kybernetika (2021)

  • Volume: 57, Issue: 3, page 546-566
  • ISSN: 0023-5954

Abstract

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In this paper, for a class of the complex nonlinear system control problems, based on the two-person zero-sum game theory, combined with the idea of approximate dynamic programming(ADP), the constrained optimization control problem is solved for the nonlinear systems with unknown system functions and unknown time-varying disturbances. In order to obtain the approximate optimal solution of the zero-sum game, the multilayer neural network is used to fit the evaluation network, the execution network and the disturbance network of ADP respectively. The Lyapunov stability theory is used to prove the uniform convergence, and the system control output converges to the neighborhood of the target reference value. Finally, the simulation example verifies the effectiveness of the algorithm.

How to cite

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Xingjian, Fu, and Zizheng, Li. "Neural network optimal control for nonlinear system based on zero-sum differential game." Kybernetika 57.3 (2021): 546-566. <http://eudml.org/doc/298173>.

@article{Xingjian2021,
abstract = {In this paper, for a class of the complex nonlinear system control problems, based on the two-person zero-sum game theory, combined with the idea of approximate dynamic programming(ADP), the constrained optimization control problem is solved for the nonlinear systems with unknown system functions and unknown time-varying disturbances. In order to obtain the approximate optimal solution of the zero-sum game, the multilayer neural network is used to fit the evaluation network, the execution network and the disturbance network of ADP respectively. The Lyapunov stability theory is used to prove the uniform convergence, and the system control output converges to the neighborhood of the target reference value. Finally, the simulation example verifies the effectiveness of the algorithm.},
author = {Xingjian, Fu, Zizheng, Li},
journal = {Kybernetika},
keywords = {zero-sum game; nonlinear system; neural network; approximate dynamic programming},
language = {eng},
number = {3},
pages = {546-566},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Neural network optimal control for nonlinear system based on zero-sum differential game},
url = {http://eudml.org/doc/298173},
volume = {57},
year = {2021},
}

TY - JOUR
AU - Xingjian, Fu
AU - Zizheng, Li
TI - Neural network optimal control for nonlinear system based on zero-sum differential game
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 3
SP - 546
EP - 566
AB - In this paper, for a class of the complex nonlinear system control problems, based on the two-person zero-sum game theory, combined with the idea of approximate dynamic programming(ADP), the constrained optimization control problem is solved for the nonlinear systems with unknown system functions and unknown time-varying disturbances. In order to obtain the approximate optimal solution of the zero-sum game, the multilayer neural network is used to fit the evaluation network, the execution network and the disturbance network of ADP respectively. The Lyapunov stability theory is used to prove the uniform convergence, and the system control output converges to the neighborhood of the target reference value. Finally, the simulation example verifies the effectiveness of the algorithm.
LA - eng
KW - zero-sum game; nonlinear system; neural network; approximate dynamic programming
UR - http://eudml.org/doc/298173
ER -

References

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