Controlling Interacting Systems in Noisy Environments

Abstract

Abstract : The objective of this project is to develop concepts for the analysis of the dynamics of interacting systems in a noisy environment. New approaches should lead to a better understanding of system dynamics and generate novel efficient algorithms of stochastic optimal control for interacting systems. One of the central issues that we address is dynamics of noise-induced switching. The phenomenon underlies a large portion of all significant changes that occur in systems in noisy environment. Examples range from breakdown events in complex systems to swarming in systems of interacting vehicles to overcoming barriers by such vehicles. Therefore understanding the switching dynamics is instrumental for developing highly efficient ways of controlling noisy systems. Central to the theoretical approach is the notion that the dynamical trajectories followed in switching form narrow tubes. We demonstrate that the tubes can be directly observed in experiment. Quantitatively, the tubes are characterized by the distribution of trajectories. To find it theoretically we modify the instanton technique developed in a completely different area, the quantum field theory. This approach maps the problem of most probable switching trajectories in noisy dissipative systems onto a problem of Hamiltonian dynamics of an auxiliary system of a higher dimension.