Approximate solution of Hamilton-Jacobi inequality by neural networks

This paper discusses a problem of solving Hamilton-Jacobi inequality which is a main difficulty in nonlinear H∞ control application. A neural networks approach is presented to obtain an approximate solution of Hamilton-Jacobi inequality. It will be shown that the problem can be formulated as a maximum value function optimization problem and then be solved by the proposed learning algorithm. The algorithm is developed based on nondifferentiable optimization theory. The effectiveness of the proposed method is demonstrated by numerical examples.