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Book Review: Advanced Robotics and Intelligent Machines:

mappings. Wang describes an analytic approach to the analysis of fuzzy systems, in particular their approximation capabilities. Based on those results, for applications in fuzzy control, at least in principle, the stability can be evaluated. Fuzzy systems are universal approximators and bear close similarities to neural networks but with the advantage of an input-output description in terms of fuzzy sets and rules. In this context one should mention the books by Brown and Harris, Southampton University, published by Prentice Hall and World Scientific. They describe similar approaches to neurofuzzy systems and control, using B-splines rather than Gaussian basis functions. Part III of the book introduces four methods for the design of fuzzy systems. Sincea 'common sense' IF-THEN rule analysis and design in the context of dynamic, possibly nonlinear systems is difficult, if not impossible, the book describes methods for learning rules and parameters based on input-output training data. The next three parts of the book concentrate on fuzzy control and apply previously introduced concepts to problems in control and signal processing. As with neural networks, it is difficult to design exercises for a taught course on fuzzy systems and fuzzy control. Consequently many exercises reduce to a proof of a small aspect of a fuzzy system or the student is required to verbally describe his solution rather than mathematically solving it. Many 'design exercises' are essentially simulations, requiring either programming skills or a simulation package like MATLAB with a toolbox that provides predefined functions for fuzzy systems modelling and simulation. The systems described include the 'backing up a truck' problem, chaotic time series prediction, the equalisation of non-linear communication channels, a cement kiln process, the 'ball-and-beam' system, the 'inverted pendulum', as well as some non-linear, time-varying and chaotic processes for control. Unfortunately, for some examples, to reconstruct simulation results, one requires some of Wang's papers or his previous book. Finally, a number of topics like fuzzy clustering for pattern recognition, fuzzy relation equations, fuzzy arithmetic, fuzzy linear programming, and possibility theory are briefly introduced. Again, the presentation is suitable for teaching and make the book a comprehensive guide to all aspects of fuzzy theory and applications in control engineering, and signal processing. Even though the parts III to IV follow closely Wang's own research results, the first part of the book provides an excellent introduction to fuzzy systems and thus a good basis to study the many other approaches proposed. OLAF WOLKENHAUER Control Systems Centre, UMIST