**Structure and Dynamics in Collectives**

**Speaker:** P. S. Krishnaprasad, University of Maryland

**Series:** Baetjer Colloquium

**Location:**
Bowen Hall Room 222

**Date/Time: **Friday, April 20, 2012, 3:30 p.m.
- 4:30 p.m.

**Abstract:**

Even a casual observer cannot but wonder about the inner dynamics at work in the agile choreography of a flock of starlings overhead that successfully eludes repeated attacks of a peregrine falcon. What are the laws that govern the steering inputs of a starling leading to such fluid-like collective motion? Can we synthesize similar abilities in aerial robotic flocks? In this talk, we explore how ideas of geometrical character offer useful perspectives in answering such questions: for example, through investigation of the structure of configuration space; the synthesis of control strategies; the role of symmetries and reduction in closed loop dynamics; and the analysis of empirical data from biology. We will illustrate our approach in these directions, using some low dimensional examples. We will examine nonlinear smoothing schemes to assimilate sampled observations of collectives of continuous time dynamical systems, e.g. bird flocking events, into generative models with continuous time (steering) inputs and outputs. The purpose of such assimilation is to evaluate hypotheses of interest, based on correlations, delays, and mechanisms of interaction between elementary units of the observed population. Appeal to the maximum principle of Pontryagin leads to alternative computational schemes, and questions of integrability of extremals, of broader mathematical interest.

**Biography:**

P. S. Krishnaprasad received the Ph.D. degree from Harvard University in 1977. He taught in the Systems Engineering Department at Case Western Reserve University from 1977 to 1980. Since August 1980, he has been with the University of Maryland, currently a Professor of Electrical & Computer Engineering, with a joint appointment at the Institute for Systems Research. His interests lie in the areas of geometric control theory, filtering and signal processing, robotics, acoustics, and biologically-inspired approaches to control, sensing and computation. His work is now focused on pursuit and cohesion in nature and in engineered systems. He is a Fellow of the IEEE. He delivered the Munich Mathematical Colloquium Lecture in fall 2006, and the Hendrik W. Bode Lecture of the IEEE Control Systems Society in 2007.