Design of Robust Adaptive Control

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Robust adaptive control is one of the most promising and most active research areas in systems and control theory. During the last two years major causes of nonrobust behavior have been discovered and means to counteract instability mechanisms have been recommended. A sharp stability-instability boundary can now be determined using a signal dependent criterion. To extend the validity of this linearized result, the concept of a slow integral manifold is proposed. This concept will be used as a nonlinear geometric-asymptotic tool in the research. The goal of this research is to employ a priori information about the plant and signals in order to reduce the complexity of the adaptive controller and thus improve its robustness. This is to be achieved by removing matchability and positive realness assumptions and allowing problem specific reduced parameterizations. A pseudo- gradient approach will be developed to guarantee local convergence. The practically guaranteed region of convergence will then be maximized by nonlinear geometric -asymptotic methods, including an analysis of in-manifold and off-manifold bounds. A preliminary pseudo-gradient scheme is described as a possible starting point for more general designs.