Chapter 6 - Identification of Nonlinear Dynamical Systems Using Neural Networks

Abstract

This chapter is concerned with the identification of a finite-dimensional discrete-time deterministic nonlinear dynamical system using neural networks. The main objective of the chapter is to propose specific neural network architectures that can be used for effective identification of a nonlinear system using only input-output data. The state space model offers a more compact representation. However, learning such a model involves the use of dynamic backpropagation, which is a very slow and computationally intensive algorithm. Both recurrent and feedforward models are considered and analyzed theoretically and practically. The main result of the chapter is the establishment of input-output models using feedforward networks. The fact that generic observability is a generic property of systems implies that almost all systems can be identified using input-output models and hence realized by feedforward networks. Throughout the chapter, simulation results are included to complement the theoretical discussions.