Neural Network Model for Constructing Feedback in Nonlinear Control Systems Based on Asymptotic Methods and the SDRE Approach

Here the problem of nonlinear control system stabilization is considered. By presenting the model of a nonlinear control system with a parameter that changes over a certain interval in a formally linear form with state dependent matrices and by introducing a quadratic quality criterion the SDRE approach is applied. Then a neural network model is built to determine a suboptimal controller based on the use of asymptotic and Padé approximations of the matrix Riccati equation solution. It is based on the procedure for selecting the best approximation option and methods for the improvement of the obtained solution (for example, splines) and takes into account the specifics of problem classes.