PECASE: Analysis and Design of Discontinuity-Driven Bifurcations

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Proposal Title: PECASE: Analysis and Design of Discontinuity-Driven BifurcationsInstitution: Virginia Polytechnic Institute and State UniversityThis award focuses on the analysis and design of nonsmooth dynamical systems, characterized by abrupt and discontinuous changes in the systems' properties, and commonly encountered in mechanical, biological, and electronic models. Of particular significance are the potentially dramatic changes in character and stability of motions of such systems that occur at the onset of weak interactions with the environment, here referred to as discontinuity-driven bifurcations. For example, in the case of human gait, premature, low-velocity ground contact of the swing foot may result in loss of stability of the sustained gait and subsequent fall, particularly in individuals with muscular disorders or the elderly. The objectives of this project are to develop a comprehensive predictive methodology for discontinuity-driven bifurcations of recurrent and transient motions and to formulate design criteria for reducing or eliminating the detrimental effects of unintentional collisions between a mechanical subsystem and its surrounding environment -- in particular, the prevention of fall-related injury due to premature ground contact during gait. The research work will closely integrate with an effort to develop a closed-ended-design course at the junior level emphasizing performance verification tests for mechatronic systems and the evaluation of a system's response in the presence of smooth and discontinuity-driven bifurcations.This project was originally funded as a CAREER award, and was converted to a Presidential Early Career Award for Engineers and Scientists (PECASE) award in September 2004.