Fractional neural network models for nonlinear Riccati systems

In this article, strength of fractional neural networks (FrNNs) is exploited to find the approximate solutions of nonlinear systems based on Riccati equations of arbitrary order. The feed-forward artificial FrNN are used to develop the energy function of the system by defining an error function in mean square sense. Design parameters for optimization of the energy function are adapted using viable local search with interior point methods (IPMs). The performance of design methodology in terms of accuracy and convergence is analyzed for two different variants of the nonlinear system. Comparison of the results with the exact solutions, as well as approximate numerical results, illustrates the correctness of the methodology. The worth of the scheme is established through statistical inferences based on a large number of simulation runs.