Optimal Control of Multiagent Decision-Making Based on Competence Evolution

We employ the theory of rarefied gas dynamics and optimal control to investigate the kinetic model of decision-making. The novelty of this paper is that we develop a kinetic model that takes into account both the influence of agents’ competence and managers’ control on decision-making. After each interaction, in addition to the changes in decision directly caused by communication with other agents, the agents’ competence evolves and indirectly influences the degree of decision adjustment through the compromise function. By adding a control term to the model, the behavior of the managers who require the group to establish consensus is also described, and the concrete expression of the control term that minimizes the cost function is obtained by model predictive control. The Boltzmann equation is constructed to characterize the evolution of the density distribution of agents, and the main properties are discussed. The corresponding Fokker–Planck equation is derived by utilizing the asymptotic technique. Lastly, the direct simulation of the Monte Carlo method is used to simulate the evolution of decisions. The results indicate that the agents’ competence and managers’ control facilitate the consistency of collective decisions.