  We study the problem of model predictive control (MPC) for the fish schooling
model proposed by Gautrais et al. (Annales Zoologici Fennici, 2008). The high
nonlinearity of the model attributed to its attraction/alignment/repulsion law
suggests the need to use MPC for controlling the fish schooling's motion.
However, for large schools, the hybrid nature of the law can make it
numerically demanding to perform finite-horizon optimizations in MPC.
Therefore, this paper proposes reducing the fish schooling model for
numerically efficient MPC; the reduction is based on using the weighted average
of the directions of individual fish in the school. We analytically show how
using the normalized eigenvector centrality of the alignment-interaction
network can yield a better reduction by comparing reduction errors. We confirm
this finding on the weight and numerical efficiency of the MPC with the
reduced-order model by numerical simulations. The proposed reduction allows us
to control a school with up to 500 individuals. Further, we confirm that
reduction with the normalized eigenvector centrality allows us to improve the
control accuracy by factor of five when compared to that using constant
weights.
