Model predictive control paradigms for fish growth reference tracking in precision aquaculture

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 feeding rate, temperature, and dissolved oxygen. This paper provides a comparative study of four model predictive control (MPC) strategies for fish growth reference tracking under a representative bioenergetic growth model in precision aquaculture. We propose to evaluate four 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 optimizes the feed conversion ratio (FCR), which is the ratio between food quantity and fish weight gain at each sampling time. This FCR-like optimization strategy minimizes the feed while maximizing the predicted 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 food cost. The last MPC formulation aims to maximize the fish growth rate while minimizing the costs. Numerical simulations that integrate a realistic bioenergetic fish growth model of Nile tilapia (Oreochromis niloticus) are illustrated to examine the comparative performance of the four proposed optimal control strategies. A sensitivity analysis is conducted to study the robustness of these MPC strategies with respect to the effect of the prediction horizon, the regularization term, and the additive input disturbances to the process. The obtained results show great potential and flexibility to meet the fish farmers’ needs depending on the type of fish, selling price, culture duration, and feed cost.