Research Initiation: Design of Robust and Multivariable Adaptive Control Systems - (REU SUPPLEMENT)

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The objective of the project is to study problems related to the design of robust and multivariable adaptive control systems. Robustness is defined as the ability of an algorithm to maintain stability in the presence of disturbances and unmoldeled dynamics. We plan to apply averaging methods to study the relationship between robustness and the error equation used for adaptation. The existence and location of the tuned values will be investigated. These values determine where the controller parameters converge in the presence of unmodeled dynamics. The analysis is expected to lead to a better understanding of robustness in adaptive control, and to suggest new approaches for design. We will also be concerned with the design of multivariable adaptive control systems. We plan to study parameterizations which guarantee parameter convergence to a unique point, and require a minimal number of parameters. These properties are desirable for convergence, robustness, and implementation considerations. The prior information needed to design multivariable adaptive control systems will also be investigated, together with ways to obtain this information from input/output measurements. Experiments will be carried out to validate the results of the theory, and motivate new problems. We expect that the research will contribute to improve design methodologies for adaptive control systems, and to a wider application of these methods.