Monday, December 8, 2014 - 3:30pm to 4:30pm
Spatially distributed dynamical systems can exhibit rich and complex phenomena, especially when the effects of uncertain environments are taken into account. The effects of this “ambient uncertainty” can sometimes be described in terms of open dynamical systems, where exogenous disturbances and perturbations produce qualitative changes in dynamical behavior compared to the closed, or isolated, system model. Several case studies from seemingly disparate fields will be presented to highlight this contrast between closed and open dynamical systems. One class of systems include vehicular formations on automated highways, flocking, gossip algorithms, and more generally coordinated control of networks. It turns out that in the limit of large-scale regular networks, there are fundamental scaling laws the characterize the ultimate controllability of such networks. The dependency of these limits on network topology is revealed by considering systems operating in uncertain environments. Connections with the theory of harmonic solids and resistive lattices will be presented. The other class of problems come from wall-bounded shear flow transition and turbulence. The open systems view provide a new perspective in which susceptibility to ambient uncertainty such as wall roughness and vibrations constitutes a transition mechanism distinct from initial condition instabilities.