具有不确定速度和需求的输运方程的最优流入控制
Optimal Inflow Control for Transport Equations with Uncertain Velocities and Demand
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中文总结 AI 辅助
该研究针对受时变下游需求和输运速度不确定性影响的线性输运方程，推导了最优流入控制，分析了误差分解、平均速度代理的性能界及最优控制的稳定性，数值实验验证了相关结果。
中文摘要 AI 辅助
我们研究受时变下游需求和输运速度不确定性影响的线性输运方程的最优流入控制。随机速度会引发随机传播时间，从而改变流入决策与其到达时刻观测到的需求之间的关系。针对固定的下游观测窗口，我们在连续时间设定下以及分段常数控制的情形中推导了显式最优控制。我们将不可约随机误差分解为需求和速度不确定性的贡献，证明速度不确定性的贡献可得到与速度方差线性相关的界。作为计算上有吸引力的替代方案，我们分析了确定性平均速度代理，其额外性能损失可得到高阶界。我们还建立了最优控制关于Wasserstein距离下速度律扰动的Lipschitz稳定性。数值实验验证了分析结果，并研究了超出线性理论的不确定非局部输运模型的代理策略。
英文摘要
We study optimal inflow control for a linear transport equation subject to uncertainty in both time-dependent downstream demand and transport velocity. The random velocity induces a random travel time and thereby changes the relation between an inflow decision and the demand observed at its arrival time. For a fixed downstream observation window, we derive explicit optimal controls in the continuous-time setting and for piecewise constant controls. We decompose the irreducible stochastic error into contributions from demand and velocity uncertainty and show that the latter admits a bound that is linear in the velocity variance. As a computationally attractive alternative, we analyze a deterministic mean-velocity proxy whose additional performance loss admits a higher-order bound. We also establish Lipschitz stability of the optimal control with respect to perturbations of the velocity law in the Wasserstein distance. Numerical experiments illustrate the analytical results and investigate the proxy strategy for an uncertain nonlocal transport model beyond the linear theory.
发表机构
- University of Mannheim（曼海姆大学）
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