Suykens J.A.K., Vandewalle J.P.L., De Moor B.L.R. Artificial Neural Networks for Modelling and Control of Non-Linear Systems

Springer, 1996, -316 p.The topic of this book is the use of artificial neural networks for modeling and control purposes. The relatively young field of neural control, which started approximately ten years ago with Barto's broomstick balancing experiments, has undergone quite a revolution in recent years. Many methods emerged including optimal control, direct and indirect adaptive control, reinforcement learning, predictive control etc. Also for nonlinear system identification, many neural network models and learning algorithms appeared. Neural network architectures like multilayer perceptrons and radial basis function networks have been used in different model structures and many on- or off-line learning algorithms exist such as static and dynamic backpropagation, prediction error algorithms, extended Kalman filtering, to name a few.
The abundance of methods is basically due to the fact that neural network models and control systems form just another class of nonlinear systems, and can of course be approached from many theoretical points of view. Hence, for newcoming people, interested in this area, and even for experienced researchers it might be hard to get a fast and good overview of the field. The aim of this book is precisely to present both classical and new methods for nonlinear system identification and neural control in a straightforward way, with emphasis on the fundamental concepts.
The book results from the first author's Ph.D. thesis. One major contribution is the so-called 'NL_q theory', described in Chapter 5, which serves as a unifying framework for stability analysis and synthesis of nonlinear systems that contain linear and static nonlinear operators that satisfy a sector condition. NL_q systems are described by nonlinear state space equations with q layers and hence encompass most of the currently used feedforward and recurrent neural networks. Using neural state space models, the theory enables to design controllers based upon identified models from measured input/output data. It turns out that many problems arising in neural networks, systems and control can be considered as special cases of NL_q systems. It is also shown by examples how different types of behaviour, ranging from globally asymptotically stable systems, systems with multiple equilibria, periodic and chaotic behaviour can be mastered within NL_q theory.Artificial Neural Networks: Architectures and Learning Rules
Nonlinear System Identification using Neural Networks
Neural Networks for Control
NL_q Theory
General Conclusions and Future Work
A: Generation of n-double Scrolls
B: Fokker-Planck Learning Machine for Global Optimization
C: Proof of NL_q Theorems