论文标题
稳定具有乘法噪声的非线性药物的最佳密度控制
Stabilizing Optimal Density Control of Nonlinear Agents with Multiplicative Noise
论文作者
论文摘要
用乘法噪声控制连续的时间动力学是随机最佳控制中的经典主题。这项工作解决了设计无限的地平线最佳控制的问题，并保证了\ textIt {单个代理或大种群系统}相同的，非合作和非网络的代理，并通过乘法噪声激发了多维和非线性和非线性随机动力学。对于属于可逆扩散过程类别的代理动力学，我们提供了对状态和控制成本功能的约束，这些函数可以保证在单个最佳控件的作用下闭环系统的稳定性。引入了与状态依赖性控制成本和波动性有关的条件，以证明平衡密度的稳定性。此条件是使用路径积分Feynman-kac公式来计算控件所需的约束的特殊情况。我们研究了稳定最佳控制与路径积分形式主义之间的联系，这使我们达到了仅根据所需平衡密度表示的控制定律公式。
Control of continuous time dynamics with multiplicative noise is a classic topic in stochastic optimal control. This work addresses the problem of designing infinite horizon optimal controls with stability guarantees for \textit{a single agent or large population systems} of identical, non-cooperative and non-networked agents, with multi-dimensional and nonlinear stochastic dynamics excited by multiplicative noise. For agent dynamics belonging to the class of reversible diffusion processes, we provide constraints on the state and control cost functions which guarantee stability of the closed-loop system under the action of the individual optimal controls. A condition relating the state-dependent control cost and volatility is introduced to prove the stability of the equilibrium density. This condition is a special case of the constraint required to use the path integral Feynman-Kac formula for computing the control. We investigate the connection between the stabilizing optimal control and the path integral formalism, leading us to a control law formulation expressed exclusively in terms of the desired equilibrium density.
