Stabilization of Nonlinear Control Systems through Using Zobov’s Theorem and Neural Networks

Authors
A Soleymanpour Bakefayat
N Dastranj
Department of Mathematical Sciences, Payame Noor University, Iran
10.29252/mmr.1.1.51
Abstract
Zobov’s Theorem is one of the theorems which indicate the conditions for the stability of a nonlinear system with specific attraction region. We have applied neural networks to approximate some functions mentioned in Zobov’s theorem in order to find the controller of a nonlinear controlled system whose law in a mathematical manner is difficult to make. Finally, the effectiveness and the applicability of the proposed method are demonstrated through using numerical examples.
Keywords
Nonlinear control systems
Stabilization
artificial neural networks
Zobov’s Theorem
Nelder-Meed Optimization
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