Robustness Quantification and Performance Improvement in Adaptive Control Systems

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The aim of the research outlined in this proposal is two-fold. First, we intend to develop a systematic quantitative theory for the design and analysis of robust adaptive control schemes. The second objective is to develop a methodology for studying and improving the transient performance of adaptive control schemes, as also alleviating erratic steady state behaviour such as bursting. The objectives mentioned above relate to two of the outstanding problems in the area of adaptive control. None of the existing theory (Lyapunov approach, persistence of excitation, etc.) can solve these problems in a practical or satisfactory manner. The lack of such results is a major stumbling block that engineers invariably encounter in attempting to put the results of adaptive control theory to practice. The methods we plan to use are based on recently obtained breakthroughs in robust parametric stability (Kharitonov's Theorem and its extensions, calculation of parametric stability margins, connections between parametric and unstructured (Hoo) perturbations) and parameter- error compensation methods. We are motivated by the possibility of exploiting these recent results in robust parametric (nonadaptive) stability and control to obtain non-conservative (practically useful) stability margins for adaptive systems, and to develop effective design schemes for robust adaptive control. Though the robust adaptive control problem is much more difficult than the corresponding nonadaptive one, the payoff is that the results obtained are likely to be more useful.