The trouble with imaginary eigenvalues. Optimal control, controllability, frequency response

Controllability of linear systems on solvable Lie groups

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies controllability by taking in consideration the eigenvalues of an associated derivation D. When the state space is a solvable connected Lie group, controllability of the systems is guaranteed if the reachable set of the neutral element is open and the derivation D has only pure imaginary eigenvalues. For bounded systems on nilpotent Lie groups such conditions are also necessary.

双线性可控性研究：线性KdV-薛定谔方程

Bilinear controllability for the linear KdV-Schr{ö}dinger equation

本文研究了线性KdV-薛定谔方程在单维环面上通过纯虚双线性控制的可控性，证明了在L2(T)中有限傅里叶模的局部时间全局近似可控性，通过饱和方法结合相乘控制与环面微分流形生成运输算子，实现全局近似可控性。

制冷系统的最优控制分析与实用NMPC应用

Optimal control analysis and Practical NMPC applied to refrigeration systems

本研究针对机械压缩制冷系统，提出基于移动边界法的降阶模型，分析其可控性，并通过仿真对比实用NMPC与反馈加前馈策略，发现两者均难以达到最优循环。

环面$\u211D^d$上薛定谔方程的可控子空间与实部可观性

Controllable subspaces and real-part observability for Schrödinger equations on $\mathbb T^d$

本文研究环面$\u211D^d$上实部控制的薛定谔方程内部可控性，刻画了最大零可控子空间，证明不可控方向为纯虚定常模式，通过实部紧性-唯一性等论证建立可观性不等式，为相关问题提供了显式描述。

复杂网络的最小能量控制

Minimum energy control for complex networks

本文研究复杂网络的最小能量控制问题，提出基于节点出度与入度比的控制策略，降低控制成本。