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Characterizing the Performance of Nonlinear Differential Operators

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Final rept. 7 Jun 2009-7 May 2012

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Highly complex behavior is common in both the natural and technological world. Nonlinear differential operators play an essential role in enabling accurate modeling and prediction of this behavior. Nonlinear systems theory provides a mathematical framework for the analysis and design of networks of these operators, thereby providing the foundation for scientists and engineers to understand and control this highly complex behavior. This project is primarily concerned with the development of analysis and computational tools that can accurately characterize the performance of specific classes of nonlinear differential operators in capturing specific behavioral properties of interest. A secondary concern is the development of controller synthesis tools that enable the design of networks of differential operators so as to yield specific behavioral properties. At the completion of this project after three years of funding, outcomes of this project include the development of new theoretical and computational tools for performance bound verification, tight performance bound characterization, and controller synthesis for representative behavioral properties. Integral-input-to-integral-output, integral-input-to-output, and input-to-state stability properties have been specifically considered. Substantial effort has been invested in the development of tools for the numerical approximation of solutions to the attendant optimization and optimal control problems. This includes computational tools utilizing approximating Markov chain methods and max-plus methods. The research undertaken is documented in 26 scholarly publications 17 published or accepted to be published, 9 in press or in review, and communicated via numerous presentations including 14 invited at internationally renowned meetings and academic institutions.

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  • Theoretical Mathematics

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