P. S. Krishnaprasad
Department of Electrical and Computer Engineering and ISR
In this talk we will discuss methods to assimilate sampled observations of collectives of continuous time dynamical systems (e.g. predator-prey encounters, bird flocking events) into generative models with continuous time inputs and outputs. The purpose of such assimilation is to assess properties of interest (such as correlations, delays, mechanisms of interaction between elementary units of the observed population). We will discuss models (based on moving frames) and methods (based on nonlinear programming) for this problem of reconstructing collectives. An alternative formulation and appeal to the maximum principle of Pontryagin, leads to novel variational problems of Subriemannian type, and questions of explicit computation of extremals.