FAILURES OF ADAPTIVE CONTROL THEORY AND THEIR RESOLUTION BRIAN D. O. ANDERSON Dedicated to Professor Thomas Kailath on his 70th birthday Abstract. Adaptive control is a very appealing technology, at least in principle. Yet its use has been conditioned by an attitude of distrustfulness on the part of some practitioners. In this paper, we explain why such distrustfulness is warranted, by reviewing a number of adaptive control approaches which have proved deficient for some reason that has not been immediately apparent. The explanation of the deficiencies, which normally were reflected in unexpected instabilities, is our main concern. Such explanations, coupled with remedies for avoiding the deficiencies, are necessary to engender confidence in the technology. These include the unpredictable failure of the MIT rule the bursting phenomenon, and how to prevent it the Rohrs’ counterexample, which attempted to

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