Lyapunov stabilization of the nonlinear control systems via the neural networks

In this paper, we have used a neural network to obtain an approximate solution to the value function of the HJB (Hamilton-Jacobi-Bellman) equation. Then, we have used it to stabilize the affine control nonlinear systems. The requisite control input is generated as the output of a neural network, which is trained off-line. We have designed two various neural networks, in which learning algorithm in the first one it is the steepest descent method, and in the second one is in its unconstrained optimization method. The proposed methods are compared with the traditional methods, and sometimes our methods are proved to be more efficient than the traditional methods. Numerical examples indicate the effectiveness of the proposed neural networks. (C) 2016 Published by Elsevier B.V.