Use of describing functions in analysis of systems with neural networks and dominant nonlinearities

The application of intelligent controllers such as neural networks and fuzzy controllers in technical systems is increasing. The main reason for this lies in the fact that intelligent controllers do not require knowing the exact mathematical model parameters of the controlled process. On the other hand, a great downside to this type of control is that stability cannot be proved. Technical systems often exhibit nonlinear behaviour which can be described with elementary nonlinear elements such as hysteresis and/or dead zones. This paper presents the use of the describing function as a means of analysis of systems with neural networks and dominant nonlinearities. The equivalent describing function can then be used for stability analysis using, for example, the Popov criterion.