Geodesic
Neural network optimal control for nonlinear system based on zero-sum differential game
Kybernetika, Tome 57 (2021) no. 3, pp. 546-566.

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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.
DOI : 10.14736/kyb-2021-3-0546
Classification : 91A80, 93C10, 93D21
Keywords: zero-sum game; nonlinear system; neural network; approximate dynamic programming 
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     title = {Neural network optimal control for nonlinear system based on zero-sum differential game},
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Xingjian, Fu; Zizheng, Li. Neural network optimal control for nonlinear system based on zero-sum differential game. Kybernetika, Tome 57 (2021) no. 3, pp. 546-566. doi : 10.14736/kyb-2021-3-0546. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2021-3-0546/

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