ncku-talk2013-12-19

NCTS(South) Seminar

DATE 2013-12-19　15:10-16:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Epstein Family Professor Jong-Shi Pang（Department of Industrial and Systems Engineering, University of Southern California）

TITLE Differential Variational Systems: A New Paradigm of Constrained Dynamical Systems

ABSTRACT This talk presents a new paradigm of constrained dynamical systems that we call a differential variational system. Such a system comprises an ordinary differential equation parameterized by an algebraic variable that is constrained to be a solution of a finite-dimensional state-dependent variational inequality. A differential variational system provides a very broad, unifying modeling framework for many special cases, including a differential algebraic equation, an optimal control problem with state-control constraints, a constrained differential Nash game, a hybrid switch system of a certain kind, as well as all biological, systems undergoing time evolution and subject to activation or de-activation of constraints. Many challenging mathematical issues arise as a result of the differential and variational features of such a system, requiring new treatment combining both classical theory of ordinary differential equations and results of contemporary optimization and variational inequalities. A summary of such issues will be presented and a touch of some selected results will be discussed.

NCTS(South) Seminar

DATE	2013-12-19　15:10-16:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Epstein Family Professor Jong-Shi Pang（Department of Industrial and Systems Engineering, University of Southern California）

TITLE	Differential Variational Systems: A New Paradigm of Constrained Dynamical Systems

ABSTRACT	This talk presents a new paradigm of constrained dynamical systems that we call a differential variational system. Such a system comprises an ordinary differential equation parameterized by an algebraic variable that is constrained to be a solution of a finite-dimensional state-dependent variational inequality. A differential variational system provides a very broad, unifying modeling framework for many special cases, including a differential algebraic equation, an optimal control problem with state-control constraints, a constrained differential Nash game, a hybrid switch system of a certain kind, as well as all biological, systems undergoing time evolution and subject to activation or de-activation of constraints. Many challenging mathematical issues arise as a result of the differential and variational features of such a system, requiring new treatment combining both classical theory of ordinary differential equations and results of contemporary optimization and variational inequalities. A summary of such issues will be presented and a touch of some selected results will be discussed.