  In precision aquaculture, the primary goal is to maximize biomass production
while minimizing production costs. This objective can be achieved by optimizing
factors that have a strong influence on fish growth, such as the feeding rate,
temperature, and dissolved oxygen. This paper provides a comparative study of
three model predictive control (MPC) strategies for fish growth reference
tracking under a representative bioenergetic growth model in precision
aquaculture. We propose to evaluate three candidate MPC formulations for fish
growth reference tracking based on the receding horizon. The first MPC
formulation tracks a desired fish growth trajectory while penalizing the feed
ration, temperature, and dissolved oxygen. The second MPC optimization strategy
directly penalizes the feed conversion ratio (FCR), which is the ratio between
food quantity and fish weight gain while minimizing the actual growth state's
deviation from the given reference growth trajectory. The third MPC formulation
includes a tradeoff between the growth rate trajectory tracking, the dynamic
energy and the cost of food. Numerical simulations that integrate a realistic
bioenergetic fish growth model of Nile tilapia (Oreochromis niloticus) are
illustrated to examine the comparative performance of the three proposed
optimal control strategies.
