Drift Instabilities in Underexcited Adaptive Systems

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Adaptive control algorithms presently dominating the theoretical literature have recently been demonstrated to behave poorly when assumptions used to prove their idealized behavior are violated. Though such violations undoubtedly occur in practice, adaptive controllers have been repeatedly documented as successful in a variety of applications. This research will focus on eliminating the theory-practice gap due to the impractical, current theoretical limitation that the controller structure be sufficient to arbitrarily modify all modes of the plant behavior. Thus, the aim of this research is the development of a theoretical framework for describing, and subsequently improving, the robustness of restricted complexity adaptive controllers. The major directions to be pursued are the characterization of undesirable parameter estimate drift in restricted complexity adaptive control as well as generation and evaluation of algorithm fixes given improved understanding of stability/instability mechanisms in existing algorithms.