The objective of this program is to investigate dynamics and control issues of complementarity systems from a hybrid system perspective with applications to engineering and biological systems. Various physical, biological and economic systems are subject to inequality constraints that are complementary to each other, i.e., at least one of a pair of inequalities holds with equality. Such dynamical systems, called complementarity systems, constitute an important class of hybrid and switching systems in applications. Complementarity approaches, along with system and control techniques, will be exploited to address critical dynamic analysis and control design problems.
Intellectual merit: The intellectual merit lies in three aspects: (1) characterization of local switching dynamics of complementarity systems; (2) long-time switching dynamic analysis and control of piecewise smooth systems; (3) applications to contact mechanical systems, systems biology, safety verification, and dynamical optimization. The analytic results to be developed in this program will lay down a rigorous foundation for computation, analysis and design of a broad class of applied nonsmooth systems. The obtained control analysis and feedback design algorithms will be applied to emerging practical systems in robotics, biology, and electronics, and will facilitate analysis and design of complex systems.
Broader impacts: The broader impacts are: (1) This program is interdisciplinary and potentially transformative due to the fundamental nature of the focused research topics and their diverse applications, such as robotics, biomedical systems, and systems biology. (2) The proposed research will be closely integrated with educational and outreach activities, including development of graduate curriculum on nonsmooth systems, active involvement with high-school students for engineering education, undergraduates' research mentoring, and advising graduate students on research and career development through a local SIAM student chapter.
