Abstract
In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach. © 2013 IEEE.
Recommended Citation
S. Mehraeen et al., "Zero-sum Two-player Game Theoretic Formulation of Affine Nonlinear Discrete-time Systems using Neural Networks," IEEE Transactions on Cybernetics, vol. 43, no. 6, pp. 1641 - 1655, article no. 6392301, Institute of Electrical and Electronics Engineers, Dec 2013.
The definitive version is available at https://doi.org/10.1109/TSMCB.2012.2227253
Department(s)
Electrical and Computer Engineering
Second Department
Computer Science
Keywords and Phrases
Hamilton-Jacobi-Isaacs (HJI); neural networks (NNs); nonlinear discrete-time (DT) systems; optimal control
International Standard Serial Number (ISSN)
2168-2267
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.
Publication Date
01 Dec 2013
PubMed ID
24273142
