Fall 2019 GRASP Seminar Series: Anthony Bloch, University of Michigan, "Periodic orbits in hybrid, robotic and biological systems"

ABSTRACT
In this talk I will discuss the dynamics of certain systems of interest in robotics and synthetic biology and consider in particular the existence of periodic behavior. I will discuss the existence or periodic orbits quite generally in certain hybrid and cyclic systems and discuss applications to bipedal locomotion, rolling systems with impacts and biological oscillators. The talk contains application of Poincare maps and bifurcation theory. Parts of these were done in collaboration with Will Clark and Matt Kvalheim. 

Presenter's biography

My reseach interests include : Hamiltonian and Lagrangian mechanics, symplectic geometry, integrable systems (including the Toda lattice, the dispersionless Toda lattice, geodesic flows and rigid body dynamics), stability, nonholonomic systems (the motion of mechanical systems with nonintegrable constraints), the relationship between continuous and discrete flows, nonlinear control and optimal control. I study various other other topics in geometric mechanics and nonlinear dynamics including quantum dynamics and control. I am on the editorial board of a number of leading journals and Editor-Chief of the SIAM J. on Control and Optimization. I am a Fellow of the IEEE, a SIAM and AMS Fellow, and have been a Guggenheim Fellow and a Senior Fellow of the Michigan Society of Fellows and a Simons Fellow. Further details in my vita below. I served as Graduate Chair (2002-2005) and Chair (2005-2008) of the Dept. of Mathematics and am currently serving another term as Chair.