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Time-steppers and coarse-grained control of microscopic distributed processes

We present an equation-free multiscale computational framework for the design of “coarse” controllers for spatially distributed processes described by microscopic/mesoscopic evolution rules. We illustrate this framework by designing discrete-time, coarse linear controllers for a Lattice-Boltzmann (LB) scheme modelling a reaction-diffusion process (a kinetic-theory based realization of the FitzHugh-Nagumo equation in one spatial dimension). Short, appropriately initialized runs of the LB simulation are used to extract the stationary states (stable or unstable) and to estimate the information required to design the coarse controller (e.g. the action of the coarse slow Jacobian of the process).