Applied Mathematics Seminar | Peter Stechlinski, Analyzing Nonsmooth Dynamical Systems using Generalized Derivatives

M3 3103

Speaker

Peter Stechlinski, Department of Mathematics and Statistics, University of Maine

Title

Analyzing Nonsmooth Dynamical Systems using Generalized Derivatives

Abstract

A variety of problems from engineering and the life sciences exhibit a mixture of continuous and discrete behavior, with examples ranging from pharmaceutical manufacturing and wind turbines to neural activity and social contagions. Nonsmoothness can also arise from the need for nonsmooth control or from mathematical techniques that aid in simulation/optimization methods. However, the presence of any such nonsmoothness in a dynamical systems framework necessitates the development of specialized tools and theory because standard methods typically come with smoothness assumptions and rely on derivative information. In this talk, we review the landscape of nonsmooth dynamical systems, a framework that now possesses a theoretical and numerical toolkit suitable for analysis in a way that mirrors the smooth case. This toolkit provides a way to characterize generalized derivative information for a number of problems (e.g., nonsmooth ODEs, nonsmooth differential-algebraic equations, optimization-constrained ODEs) for use in design, control, optimization, etc. This approach is possible thanks to recent computationally-relevant developments in nonsmooth analysis, which will be reviewed, and is applicable to a wide range of continuous/discrete problems and applications of interest.