论文标题
无限期的二次二次平均野外社会控制问题与乘法噪声
Indefinite Linear Quadratic Mean Field Social Control Problems with Multiplicative Noise
论文作者
论文摘要
本文研究了线性二次（LQ）的统一稳定和社会最优性，平均野外控制问题与乘法噪声，其中代理是通过动力学和个人成本耦合的。成本功能中的状态和控制权重不限于半明确。这导致了不确定的LQ平均场控制问题，由于乘法噪声的深度性质，该问题仍然可以很好地置。我们首先通过变异分析获得一组向前的随机微分方程（FBSDE），并通过解耦FBSDE构建反馈控制。通过使用两个Riccati方程的解决方案，我们设计了一组分散的控制定律，进一步证明这在社会上是渐进的。在线性基质不等式的帮助下，给出了一些等效条件，以均匀地稳定系统。给出了一个数值示例来说明拟议的控制定律的有效性。
This paper studies uniform stabilization and social optimality for linear quadratic (LQ) mean field control problems with multiplicative noise, where agents are coupled via dynamics and individual costs. The state and control weights in cost functionals are not limited to be positive semi-definite. This leads to an indefinite LQ mean field control problem, which may still be well-posed due to deep nature of multiplicative noise. We first obtain a set of forward-backward stochastic differential equations (FBSDEs) from variational analysis, and construct a feedback control by decoupling the FBSDEs. By using solutions to two Riccati equations, we design a set of decentralized control laws, which is further shown to be asymptotically social optimal. Some equivalent conditions are given for uniform stabilization of the systems with the help of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed control laws.
