Model Predictive Control of Fish Schooling Model with Reduced-Order Prediction

We investigate the model predictive control (MPC) of the fish schooling model by Gautrais et al. (Annales Zoologici Fennici, 2008). The attraction/alignment/repulsion law within the model is not necessarily well-considered in the current MPC results in the systems control theory due to the high nonlinearity arising from the law. In this paper, we propose a MPC of the fish schooling model via model reduction, which is based based on taking the weighted average of the directions of individual fish in the school. It is analytically shown that using the normalized eigenvector centrality of the alignment-interaction network can yield a reduction with potentially smaller reduction error. This finding on the weight as well as the numerical efficiency of the model predictive control with the reduced-order model is confirmed by numerical simulations.