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In recent years, there has been a wide interest in non-linear adaptive control using approximate models, either for tracking or regulation, and usually under the banner of neural network based control. The authors present a unique critical evaluation of the approximate model philosophy and its setting, rigorously comparing the performance of such controls against competing designs. Analysing a very topical aspect of contemporary research and control practice, this book highlights the situations in which approximate model based designs are most appropriate and indicates scenarios in which other designs could be used more productively. Throughout the text concepts are illustrated using a variety of examples, both academic problems and those based on physical examples. The work is designed to open the door to realistic applications. It provides a unified coverage of the theory and application of a wide range of control systems areas including neural network based control and control using the approximate model. It presents a mathematically well founded introduction to the area of intelligent control.It provides a varied selection of practical examples drawn from a variety of fields, including robotics and aerospace, illustrate theoretical principles. It gives clear comparisons of a variety of control designs and offers cross disciplinary approach to this leading edge topic. It is a valuable reference for control practitioners and theorists, artificial intelligence researchers and applied mathematicians, as well as graduate students and researchers with an interest in adaptive control and stability.