Opinion control problem with average-oriented opinion dynamics and limited observation moments

In the paper, we propose a model of opinion dynamics in the presence of a center of influence. The center aims in distributing the opinion closer to the target one minimizing the costs. We consider the case when the center takes into account only some fixed number of observations from the opinion trajectory and taking into account the difference between the agent's opinion and the socially desired opinion in these periods. The dynamics of the state variable is given by a linear difference equation. The player's cost is a linear quadratic function with respect to the state variables and the player's strategy. The Euler equation method is used to find the centers optimal strategy. Numerical simulations of the theoretical results are given.