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Applied Mathematics and Sciences: An International Journal (MathSJ) ISSN: 2349 – 6223 http://airccse.com/mathsj/index.html Call for papers Applied Mathematics and Sciences: An International Journal (MathSJ) aims to publish original research papers and survey articles on all areas of pure mathematics, theoretical applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Topics of interest include, but are not limited to, the following: Abstract Algebra and Applications Adaptive control Agriculture, environment, health applications Algorithms Applications of modelling in science and engineering Artificial Neural Networks (ANN) Computational Complexity Computer modelling Control theory Differential Geometry Digital control Discrete Mathematics Embedded systems Evolutionary algorithms Fault detection and isolation Feedback control Functional Analysis Fuzzy logic and applications Fuzzy set theory Genetic Algorithms Genetic algorithms and evolutionary computing Graph Theory and Applications Hybrid systems Industry, military, space applications Linear and nonlinear control systems Linear and Nonlinear Programming Markov Chains and Applications Mathematical modelling Model predictive control Networked control systems Neural networks and fuzzy logic Neuro-Fuzzy Control Numerical Analysis Numerical analysis and scientific computing Operations Research Optimal Control Optimization and optimal control Optimization Theory Ordinary and Partial Differential Equations Process control and instrumentation Real and Complex Analysis Real-time issues Robust control Set Theory Sliding mode control Statistics Stochastic control and filtering Stochastic Modelling System identification and control Systems and automation Topology and Analysis Paper Submission Authors are invited to submit papers for this journal through E-mail: ...

In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrained by a PDE of continuity-type, governing the dynamics of the probability distribution of the agent population. We show the existence of mean field optimal controls both in the stochastic and deterministic setting. We derive rigorously the first order optimality conditions useful for numerical computation of mean field optimal controls. We introduce a novel approximating hierarchy of sub-optimal controls based on a Boltzmann approach, whose computation requires a very moderate numerical complexity with respect to the one of the optimal control. We provide numerical experiments for models in opinion formation comparing the behavior of the control hierarchy. ; ERC advanced Grant 668998 (OCLOC) ; (VLID)2523620