用于交互粒子系统设定点稳定的反馈方法
Feedback approaches for set-point stabilization of interacting particle systems
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中文总结 AI 辅助
该研究针对源于Cucker-Smale模型的交互粒子系统，采用瞬时滚动时域控制算法推导反馈，保留端口哈密顿结构，结合能量平衡证明相关收敛性，实现设定点稳定。
中文摘要 AI 辅助
我们研究将一类交互粒子系统渐近稳定至指定粒子构型且速度为零的问题，这类交互粒子系统源于平均场层面的Cucker-Smale模型。我们未通过手动求解IDA-PBC匹配方程设计反馈，而是采用瞬时滚动时域控制算法推导反馈，证明该反馈保留了交互粒子系统的端口哈密顿结构，因此可在IDA-PBC框架下得到解释。此外，闭环哈密顿的能量平衡为证明离散和连续时间下粒子速度与相互作用力的收敛性提供了重要工具；若控制算子是满射的，我们还证明了粒子位置向指定构型的收敛性。
英文摘要
We explore the problem of asymptotically stabilizing a class of interacting particle systems to a prescribed particle configuration with zero velocity. The class of interacting particle systems is motivated by the Cucker-Smale model on the mean-field level. Rather than designing a feedback by manually solving an IDA-PBC matching equation, we derive a feedback using an instantaneous rolling horizon control algorithm. We show that this feedback preserves the port-Hamiltonian structure of the interacting particle system and therefore allows for an interpretation in the IDA-PBC framework. Additionally, the energy balance of the closed-loop Hamiltonian provides an important tool to prove convergence of the particles' velocities and interaction forces in discrete and continuous time. If the control operator is surjective, we additionally prove convergence of the particle positions to the prescribed configuration.
发表机构
- Port-Hamiltonian Institute, School of Mathematics and Natural Sciences, University of Wuppertal（伍珀塔尔大学数学与自然科学学院）
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