Adaptive Stabilization Theory

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Adaptive control theory lacks a conceptual framework which is sufficiently simple to help qualified nonspecialists to understand the current theory without making an inordinately large time investment and which might also serve as the basis for further development. We propose to continue our recently initiated research program aimed at constructing such a framework. Existing adaptive algorithms for which 'global' stability can be proved without requiring sufficient excitation are either applicable to process models satisfying assumptions which recent results show are unnecessary restrictive or perform inefficiently and consequently are of limited practical value. The underlying reason for this is that to be applicable to "large" classes of process models, the parameter design models upon which certainty equivalence control is based, almost always have points in their parameter spaces at which the design model is not stabilizable--and at such points, certainty equivalence control is impossible. We propose to deal with this problem in two fundamentally different ways. First, we propose to develop and utilize new parameterized design models which are stabilizable on their parameterized spaces and, in addition, are applicable to "large" classes of process models. Second, as an alternative approach we propose to exploit the concept of "implicit tuning" which does not require a design model to be stabilizable at every point in its parameter space. In both cases we shall rely heavily on computer simulation to rule out unacceptable algorithms and to guide us in the development of acceptable ones.