About Adaptive Singular Systems with External Delay

分数阶延迟微分方程与受控弱奇异Volterra延迟积分方程的Pontryagin最大值原理

Pontryagin maximum principle for fractional delay differential equations and controlled weakly singular Volterra delay integral equations

该文研究Pontryagin最大值原理在分数阶延迟微分方程、Volterra延迟积分方程两类系统中的应用，探讨对应控制问题的最优求解方法，并辅以示例验证研究结果。

通过奇异摄动实现分布式时间变化覆盖控制

Distributed Time-Varying Coverage Control via Singular Perturbations

本文提出了一种基于奇异摄动理论的分布式时间变化覆盖控制算法，通过双时间尺度分离方法实现机器人对动态密度函数的最优部署跟踪。

离散线性时滞系统相对可控性的充分必要条件

Necessary and sufficient conditions for relative controllability of discrete linear delay systems

本文研究离散线性时滞系统的相对可控性，提出Kalman型秩条件并构造离散Gramian矩阵，进而建立相对可控性的充分必要条件，并通过数值算例验证了理论结果。

控制群集：在随机延迟下的稀疏驱动与碰撞规避

Controlling the Swarm: Sparse Actuation and Collision Avoidance under Stochastic Delay

本文提出一个统一的有限N框架，研究随机延迟下领导者-追随者粒子系统的稀疏驱动与碰撞规避问题，通过构建Lyapunov函数解决数学稳定性问题，并展示稀疏驱动在减少控制成本的同时揭示了领导者密度的非单调敏感性。

A financial market with singular drift and no arbitrage

We study a financial market where the risky asset is modelled by a geometric Itô-Lévy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier. See e.g. Jarrow & Protter for an explanation and discussion of this model in the Brownian motion case. As already pointed out by Karatzas & Shreve (in the continuous setting), this allows for arbitrages in the market. However, the situation in the case of jumps is not clear. Moreover, it is not clear what hap…

具有输入时滞的二维反应扩散方程的双边边界控制

Bilateral boundary control of an input delayed 2-D reaction-diffusion equation

针对矩形域上具有双边输入时滞的二维反应扩散方程，提出基于PDE backstepping的时滞补偿设计，构造含Volterra与仿射Volterra积分变换的新变换，处理Dirac Delta奇异核方程并完成稳定性分析与仿真验证。