The past decade has witnessed a great deal of interest in both the theory and practice of adaptive control using multiple models, switching, and tuning. The general approach was introduced in the early 1990s to cope with large and rapidly varying parameters in control systems. During the following years, detailed mathematical analyses of special classes of systems were carried out. Considerable empirical evidence was also collected to demonstrate the practical viability of the methods proposed. This paper attempts to review critically the stability questions that arise in the study of such systems, describes recent extensions of the approach to non-linear adaptive control, and discuss briefly promising new areas of research, particularly related to the location of models.

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Output tracking via the novel Stable Dynamic model Inversion (SDI) technique, applicable to non-minimum phase systems, and which naturally takes into account the presence of noise in target time histories, is considered here. We are motivated by the typical need to replicate time signals in the automobile industry. The earlier approaches to stable inversion do not satisfactorily take into account the measurement and system noise, and the zeros of the system are restricted to certain regions in the complex plane.

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