标记跳跃扩散的开环确定性密度控制
Open-loop Deterministic Density Control of Marked Jump Diffusions
摘要：
在对由其连续体密度表示的大种群、系综、多智能体系统的动态和最优控制建模中的标准实践是使用局部反馈信息对个体决策建模。与闭环最优控制方案相比，开环策略（其中集中式控制器向代理集合广播相同的控制信号）减轻了此类系统的计算和基础设施要求。本文研究了由显式跳跃扩散随机扩散方程控制的智能体密度控制的开环确定性最优控制综合问题。密度演化根据一个向前的时间Chapman-Kolmogorov偏积分微分方程和必要的最优性条件得到使用无限维最小值原理（IDMP）。建立了IDMP与动态规划原理、IDMP与随机动态规划之间的关系。使用线性Feynman-Kac引理，基于采样的算法来计算控制，并证明了代理动力学与非仿射和非线性漂移以及噪声项。
英文摘要：
The standard practice in modeling dynamics and optimal control of a large population, ensemble, multi-agent system represented by it's continuum density, is to model individual decision making using local feedback information. In comparison to a closed-loop optimal control scheme, an open-loop strategy, in which a centralized controller broadcasts identical control signals to the ensemble of agents, mitigates the computational and infrastructure requirements for such systems. This work considers the open-loop, deterministic and optimal control synthesis for the density control of agents governed by marked jump diffusion stochastic diffusion equations. The density evolves according to a forward-in-time Chapman-Kolmogorov partial integro-differential equation and the necessary optimality conditions are obtained using the infinite dimensional minimum principle (IDMP). We establish the relationship between the IDMP and the dynamic programming principle as well as the IDMP and stochastic dynamic programming for the synthesized controller. Using the linear Feynman-Kac lemma, a sampling-based algorithm to compute the control is presented and demonstrated for agent dynamics with non-affine and nonlinear drift as well as noise terms.
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