论文标题
强大的平均现场社会控制问题与分析意见动态分析中的应用
Robust Mean Field Social Control Problems with Applications in Analysis of Opinion Dynamics
论文作者
论文摘要
本文调查了具有未建模动力学的线性二次平均场控制系统的社会最佳性。代理商的目的是优化社会成本，这是所有代理商的成本之和。通过变分分析和直接解耦方法，分析了社会最佳控制问题，并为代表代理人获得了两个等效的辅助强大最佳控制问题。通过解决一致的平均场近似值的辅助问题，设计了一组分散的策略，并进一步证明了其渐近社会最优性。接下来，将结果应用于社交网络中意见动态的研究。分别对有限和无限的视野分析了意见的演变。所有观点都显示出与概率意义上的平均意见达成共识。最后，通过Graphon理论研究了多个人群之间的局部相互作用。
This paper investigates the social optimality of linear quadratic mean field control systems with unmodeled dynamics. The objective of agents is to optimize the social cost, which is the sum of costs of all agents. By variational analysis and direct decoupling methods, the social optimal control problem is analyzed, and two equivalent auxiliary robust optimal control problems are obtained for a representative agent. By solving the auxiliary problem with consistent mean field approximations, a set of decentralized strategies is designed, and its asymptotic social optimality is further proved. Next, the results are applied into the study of opinion dynamics in social networks. The evolution of opinions is analyzed over finite and infinite horizons, respectively. All opinions are shown to reach agreement with the average opinion in a probabilistic sense. Finally, local interactions among multiple populations are examined via graphon theory.
