Stable adaptive neural network control.

*(English)*Zbl 1001.93002
The Kluwer International Series on Asian Studies in Computer and Information Science (ASIS). 13. Boston: Kluwer Academic Publishers. xvi, 282 p. EUR 153.00; $ 140.00; £97.00 (2002).

Recent years have seen a rapid development of adaptive neural network control techniques and their applications. The main objective of the book is to develop stable adaptive neural control strategies and to perform transient performance analysis on the resulting neural control systems analytically. In this sense Lyapunov stability techniques play a critical role. Besides, mainly a class of single input single output (SISO) nonlinear systems, which can be rendered to the Brunovsky form, is considered. The book starts with a brief introduction to adaptive control, neural network (NN) control and the possible instability mechanisms in adaptive neural control systems in Chapter 1. Then Chapter 2 gives the brief summary of basic mathematical tools needed in the book. The next chapter presents radial basis function (RBF) NNs, which the authors call linearly parametrized NNs, and multilayer NNs, which are called nonlinearly parametrized nets. Let us mention that such a classification is not precise. In Chapter 4 the regionally stable NN design is proposed for a nonlinear system in the Brunovsky controller form. In the next chapter the integral Lyapunov function is introduced for adaptive control in the case of SISO nonlinear systems as well as for many-inputs many-outputs (MIMO) nonlinear systems. In Chapter 6, adaptive NN control is investigated for a class of nonaffine nonlinear systems. In the last Chapter 7, triangular nonlinear systems are treated using quadratic Lyapunov functions. Finally, the conclusion is proposed on the methods used in the book with a sketch of further research directions in the future.

The book is written in a good mathematical way. But unfortunately simulations are performed only for examples that are, in a sense, academic rather than for real applications. Also, it is very positive to learn that the authors are aware of some shortcomings of the method used. Namely, concerning the Lyapunov function technique, they say: “For a given nonlinear system there is in general no systematic procedure for choosing a suitable Lyapunov function to guarantee system stability.” That’s very important, as many authors in the field just mystify readers that the Lyapunov function method is an absolutely general one. The pedagogy of the book is at a high level, and one can agree with the authors that the book can be recommended to a wide readership and could be a useful reference for research students, academics, and practicing engineers in the area of neural adaptive control.

The book is written in a good mathematical way. But unfortunately simulations are performed only for examples that are, in a sense, academic rather than for real applications. Also, it is very positive to learn that the authors are aware of some shortcomings of the method used. Namely, concerning the Lyapunov function technique, they say: “For a given nonlinear system there is in general no systematic procedure for choosing a suitable Lyapunov function to guarantee system stability.” That’s very important, as many authors in the field just mystify readers that the Lyapunov function method is an absolutely general one. The pedagogy of the book is at a high level, and one can agree with the authors that the book can be recommended to a wide readership and could be a useful reference for research students, academics, and practicing engineers in the area of neural adaptive control.

Reviewer: Ladislav Andrey (Praha)

##### MSC:

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |

93C40 | Adaptive control/observation systems |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

93D30 | Lyapunov and storage functions |

93D21 | Adaptive or robust stabilization |

93B10 | Canonical structure |

93C10 | Nonlinear systems in control theory |