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Geometry of Collectives: Control, Dynamics, and Reconstruction
Start Date: 5/22/2014Start Time: 2:00 PM
End Date: 5/22/2014End Time: 3:00 PM

P. S. Krishnaprasad 
Electrical & Computer Engineering
University of Maryland
College Park

Institute of Systems Research

Phillips Hall 736

Hosted by: Dr. Taeyoung Lee (

Geometric ideas enter the investigation of collective behavior from multiple vantage points: the structure of configuration space; the synthesis of control strategies; the role of symmetry and reduction in closed loop dynamics; and the analysis of empirical data from biology. In this lecture we will present an overview of recent progress in these directions. We will consider methods to assimilate sampled observations of predator-prey encounters and bird flocking events into generative models based on differential equations with 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.  Initial ideas on the development of control strategies were strongly influenced by studies in the laboratory (with Cynthia Moss and her students), on the prey-capture behavior of echolocating bats. Strategies found in these studies serve as building blocks for rules of collective behavior. Analysis of trajectory data (provided by Andrea Cavagna) on large flocks of starlings demands efficient reconstruction techniques. Again the data on prey-capture behavior of bats is a testing ground for our methods of reconstruction. We will discuss some robotics experiments guided by these studies.

Outline of presentation:  (1) Models of individual agents (self-steering particles and matrix Lie groups); (2) Dyadic interactions as building blocks (pursuit, escape, boundary tracking); (3) Models of collectives (graphs, strategies, optimality); (4) Configuration space methods (shapes, ensemble moment of inertia, energy splitting); (5) Data assimilation (optimal fitting, cross-validation, rules for natural collectives).

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 mechanics and 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.
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