  In inertial microfluidics colloidal particles in a Poiseuille flow experience
the Segr\'e-Silberberg lift force, which drives them to specific positions in
the channel cross section. Due to the Saffman effect an external force applied
along the microchannel induces a cross-streamline migration to a new
equilibrium position. We apply optimal control theory to design the time
protocol of the axial control force in order to steer a single particle as
precisely as possible from a channel inlet to an outlet at a chosen target
position. We discuss the influence of particle radius and channel length and
show that optimal steering is cheaper than using a constant control force.
Using a single optimized control-force protocol, we demonstrate that even a
pulse of particles spread along the channel axis can be steered to a target and
that particles of different radii can be separarted most efficiently.
