No abstract

In this paper the adaptive nonlinear identification and trajectory tracking are discussed via dynamic neural networks. By means of a Lyapunov-like analysis we determine stability conditions for the identification error. Then we analyze the trajectory tracking error by a local optimal controller. An algebraic Riccati equation and a differential one are used for the identification and the tracking error analysis. As our main original contributions, we establish two theorems: the first one gives a bound for the identification error and the second one establishes a bound for the tracking error. We illustrate the effectiveness of these results by two examples: the second-order relay system with multiple isolated equilibrium points and the chaotic system given by Duffing equation.

No abstract

PrefaceDue to the big enthusiasm generated by successful applications, the use of static (feedforward) neural networks in automatic control is well established. Although they have been used successfully, the major disadvantage is a slow learning rate.Furthermore, they do not have memory and their outputs are uniquely determined by the current value of their inputs and weights. This is a high contrast to biological neural systems which always have feedback in their operation such as the cerebellum and its associated circuitry, and the reverberating circuit, which is the basis for many of the nervous system activities.Most of the existing results on nonlinear control are based on static (feedforward) neural networks. On the contrary, there are just a few publications related to Dynamic Neural Networks for Automatic Control applications, even if they offer a better structure for representing dynamic nonlinear systems.As a natural extension of the static neural networks capability to approximate nonlinear functions, the dynamic neural networks can be used to approximate the behavior of nonlinear systems. There are some results in this directions, but their requirements are quite restrictive.In the summer of 1994, the first two authors of this book were interested by The book could be used for self learning as well as a textbook. The level of competence expected for the reader is that covered in the courses of differential equations, the nonlinear systems analysis, in particular, the Lyapunov methodology, and some elements of the optimization theory. The helpful review of Dr.Vladimir Kharitonov is greatly appreciated. Thanks are also due to anonymous reviewers of our publications, on the topics matter of this book, for their constructive criticism and helpful comments.We want to thank the editors for their effective cooperation and great care making possible the publication of this book.Last, but not least, we thank the time and dedication of our wives Tatyana, Maria de Lourdes, and Xiaoou. Without them this book would not be possible.

No abstract