Adaptive control of nonlinear systems and applications

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Some physical systems are modeled by ordinary differential equations (ODE), while others must be described by differential algebraic equations (DAE). In general, DAE systems are the basic description of a number of practical processes while ODE systems are a simplification. Some DAE systems can be reduced to ODE systems. In most cases, such a simplification is not realizable. Therefore, the study of DAE systems is as significant as ODE systems. Almost all physical systems are nonlinear in nature and contain a certain amount of unknown parameters. Therefore, it is of both theoretical and practical importance to develop a nonlinear control theory for constructing controllers to achieve the control objectives and designing adaptive laws to estimate unknown parameters.     Adaptive control has been drawing great attention from control experts since the 1970s. For linear systems, the adaptive control theory has been well established, while it is far from perfect for the nonlinear counterpart. All existing adaptive control design methods have their limitations. The first objective of this research program is to improve the existing adaptive controller design methods and search for a new design technique.     The control theory of linear DAE systems has been well established. The literature on feedback control of nonlinear DAE systems is sparse. To the best of the applicant's knowledge, the adaptive control problems for DAE systems is still open. The second objective of this research program is to develop a design method for adaptive control of nonlinear DAE systems.     It is obvious that there exists a big gap between the control theory and engineering fields. The third objective is to investigate the applications of nonlinear adaptive control to robots, motors, power electronics converters, and so on, to reduce the gap between the adaptive control theory and applications.     The significance of this program lies in a possible breakthrough in the adaptive control theory for nonlinear DAE systems and applications of adaptive control theory.