CDS Invited Lecture: P. S. Krishnaprasad, Reduction, Enlargement, and Optimal Collective Behavior
Control and Dynamical Systems Invited Lecture Series
Reduction, Enlargement, and Optimal Collective Behavior
P. S. Krishnaprasad
Electrical and Computer Engineering Department
Institute for Systems Research
University of Maryland
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Meeting ID: 991 3869 0751
Roger Brockett’s 1973 paper, "Lie Theory and Control Systems Defined on Spheres," has illuminated the field through the many questions and threads of inquiry it initiated. In this talk, we consider one aspect of optimal control and Brockett’s approach to it. In joint work with Eric Justh, we had derived a synchronization result for interacting agents subject to a quadratic cost functional. We used methods of Poisson reduction and illustrated the same in the setting of the rigid motion group SE(2). On the other hand, Brockett’s approach in his 1973 paper suggests a convenient alternative, best described as enlargement. We will discuss these results and questions evolving from them.
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 control theory, filtering and signal processing, robotics, acoustics, and biologically -inspired approaches to control, sensing, and computation. His current work includes the study of natural and artificial collectives, control in statistical physics, and the geometry of human movement. He is a Fellow of the IEEE, was the Munich Mathematical Colloquium Lecturer in 2006, and was the Hendrik W. Bode Lecturer of the IEEE Control Systems Society in 2007.