Optimal Control of Fish Growth Under Uncertainty Using Chance Constraint Model Predictive Controller

Abstract

To achieve sustainability goals (social, economic and environmental), recirculation aquaculture systems (RAS) should be operated at optimal conditions. Recirculation aquaculture systems have various additive and unpredictable disturbances such as irregular temperature in big tanks, uneven distribution of feed and uncertain rate constants for nutrients utilization by fish. With such disturbance the performance of RAS cannot be met with probability one. Thus, the performance level should be attained under a desired probability (reliability) level. Therefore, in this paper we apply the chance-constraint model predictive control (CC-MPC) approach with state estimation using an Unscented Kalman Filter (UKF) to meet this requirement. The cost function is based on the feed conversion ratio metric, profit maximization with desired growth reference trajectory tracking. A bio-energetic and econometric model of fish growth in a RAS is utilized to illustrate the application of the formulation through simulations. Healthy fish growth is enabled by applying a health monitoring estimator based on artificial Intelligence (AI) in the feedback loop. The CC-MPC is compared to a deterministic MPC, with a focus on constraint breaching, computation time, and operational behavior. The simulations show similar performance for the fish growth for both types of MPC, while the computation time increases slightly for the CC-MPC, together with operational behaviors getting limited. In the case study, a final average fish weight of 433g is reached at a reliability level of 95% compared to 429g of the deterministic approach.