论文标题
平均场稀疏对具有添加剂白噪声的系统的最佳控制
Mean field sparse optimal control of systems with additive white noise
论文作者
论文摘要
我们通过对代理的选定子集（领导者）的简约干预措施（领导者）来控制具有添加剂白噪声的多代理系统的问题。对于具有SDE约束的这种受控系统，我们将严格的限制过程引入了无限维度的最佳控制问题，该问题通过与McKean-Vlasov-type SDE的领导者耦合，从而限制了ode系统的耦合，同时管理原型自行车的动力学。后者是在对初始数据分布的一些假设下，等效于（非线性抛物线）PDE-ODE系统。通过将管理方程的平均场限制与有限维度问题的成本功能的$γ$限制联系在一起，可以实现极限平均场最佳控制问题的推导。
We analyze the problem of controlling a multi-agent system with additive white noise through parsimonious interventions on a selected subset of the agents (leaders). For such a controlled system with a SDE constraint, we introduce a rigorous limit process towards an infinite dimensional optimal control problem constrained by the coupling of a system of ODE for the leaders with a McKean-Vlasov-type SDE, governing the dynamics of the prototypical follower. The latter is, under some assumptions on the distribution of the initial data, equivalent with a (nonlinear parabolic) PDE-ODE system. The derivation of the limit mean-field optimal control problem is achieved by linking the mean-field limit of the governing equations together with the $Γ$-limit of the cost functionals for the finite dimensional problems.
