Abstract
In this work we present the first systematic framework to sculpt active
nematics systems, using optimal control theory and a hydrodynamic model of
active nematics. We demonstrate the use of two different control fields, (1)
applied vorticity and (2) activity strength, to shape the dynamics of an
extensile active nematic that is confined to a disk. In the absence of control
inputs, the system exhibits two attractors, clockwise and counterclockwise
circulating states characterized by two co-rotating topological $+\frac{1}{2}$
defects. We specifically seek spatiotemporal inputs that switch the system from
one attractor to the other; we also examine phase-shifting perturbations. We
identify control inputs by optimizing a penalty functional with three
contributions: total control effort, spatial gradients in the control, and
deviations from the desired trajectory. This work demonstrates that optimal
control theory can be used to calculate non-trivial inputs capable of
restructuring active nematics in a manner that is economical, smooth, and
rapid, and therefore will serve as a guide to experimental efforts to control
active matter.