Research Initiation Award: Parameter Estimation in Adaptive Control

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The objective of the research is to analyze and quantify the design of estimators with intended application in adaptive control systems. Interest is mainly focused on certain aspects of closed-loop performance in the presence of uncertainty and, particularly, on preventing the closed loop signals from reaching excessively large magnitude for short time periods, commonly known as "burst" phenomena. Such undesirable phenomena are of great practical significance, especially in cases of poorly excited systems where the true nonlinear nature of adaptive controllers is highly pronounced. The plan is to investigate the properties of estimators whose design is performed via signal energy as well as amplitude criteria. Although the minimization of the maximum amplitude of the estimation error typically leads to a linear programming problem of increasing dimensionality, recursive suboptimal solutions will be considered in order to alleviate this problem. The preliminary investigations indicate that these techniques allow for amplitude considerations in the design of adaptive systems and for a more efficient use of the available measurements. Particular emphasis will be given to the extension of this approach to time-varying systems and the assessment of the associated performance trade-offs. It is expected that the results of the research will make a significant contribution in the design of practically acceptable adaptive controllers.