Modeling of neural networks in feedback systems using describing functions

In this article, a novel approach to modeling of neural networks in feedback systems using describing functions is proposed. Results on using describing functions for modeling of single-input single-output (SISO) neural networks with respect to an exponential input are presented. Through a simple example, it is then demonstrated that the resulting models of neural networks can be used to analytically calculate values for network weights such that the transient behavior of a feedback system embedded with a neural network can be “shaped” as desired. These results suggest that the proposed approach of using describing functions for modeling of neural networks could facilitate further theoretical analysis and synthesis of neural networks in feedback systems. Simulation conducted to verify the analytical results are described. Sources of approximation error in this proposed approach are examined, and potential applications and possible extension of the work reported in this article are discussed