考虑一个具有解耦马尔可夫转移动态和经验密度反馈的有限智能体群体，需满足以下约束：以至少 $1-δ_r$ 的概率，至少 $α_r$ 比例的智能体必须在某个时刻 $t^*$ 到达目标区域；同时，在 $t^*$ 之前的每个时刻，不安全人口比例必须以至少 $1-δ_u$ 的概率保持在 $β_u$ 以下。然而，标准平均场方法仅在期望意义上强制这些约束，未能考虑有限车队规模 $N$ 下的随机波动。为解决此控制问题，我们通过离散时间 Lyapunov 递归，将经验密度的二阶矩（方差）与平均场轨迹一同传播，并应用 Cantelli 不等式将机会约束转化为关于经验密度矩的可处理确定性条件。随后，我们将这些基于矩的替代约束纳入基于梯度的序列凸近似过程，用于密度反馈策略综合。此外，我们引入额外的矩误差界限以构建严格的有限 $N$ 证书。该方法在网格世界环境和电力系统电动汽车充电聚合问题上进行了评估，并与标准的确定性种群级线性规划基线进行了比较。

Consider a finite population of agents with decoupled Markov transition dynamics and empirical-density feedback, subject to the following constraints: with probability at least $1-δ_r$, at least a fraction $α_r$ of agents must reach a target region at some time $t^*$, while, at each time up to $t^*$, the unsafe population fraction must remain below $β_u$ with probability at least $1-δ_u$. However, standard mean-field methods enforce these constraints only in expectation, which fails to account for stochastic fluctuations at finite fleet size $N$. To address this control problem, we propagate the second-order moment (variance) of the empirical density alongside the mean-field trajectory via a discrete-time Lyapunov recursion, and apply the Cantelli inequality to convert chance constraints into tractable deterministic conditions on the moments of the empirical density. We then incorporate these moment-based surrogate constraints into a gradient-based sequential convex approximation procedure for density-feedback policy synthesis. We further introduce additional moment-error bounds to construct a rigorous finite-$N$ certificate. The method is evaluated on a gridworld environment and a power-system EV-charging aggregation problem and compared with a standard deterministic population-level LP baseline.