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. PI proposes to continue his recently initiated research program aimed at constructing such a framework. Existing adaptive algorithms of 'practical' structure for which 'global' stability can be proved without requiring sufficient excitation are only applicable to process models satisfying assumptions which recent results suggest are unnecessarily restrictive. The reason for this seems to be related to the reliance of these algorithms on an augmented error for parameter tuning. He proposes to develop algorithms which can adaptively stabilize processes under assumptions weaker than those presently required. His approach will be to use indirect control concepts, since error augmentation is not needed using this approach. He will use computer simulation experiments to rule out unacceptable algorithms and to guide him in the development of acceptable ones.