描述漂浮固体与周围流体相互作用系统的 LQR 控制
LQR control for a system describing the interaction between a floating solid and the surrounding fluid
AI总结：
针对漂浮固体与黏性浅水波耦合且因无界流体域而非指数稳定的系统，论文结合解析半群与插值证明适定性，并构建可由 Riccati 方法设计反馈控制的无限时域 LQR 问题。
摘要：
本文研究一个无限时间时域 LQR 最优控制问题，该问题所针对的系统在线性近似范围内描述漂浮固体的垂直振荡，并与其所漂浮的自由边界流体的运动相耦合。流体流动由线性化 Saint-Venant 方程（浅水区情形）的黏性版本描述。我们面临的主要困难是流体占据的区域无界，因此系统不具有指数稳定性。这一事实首先给证明适定性带来挑战，需要结合使用解析半群理论与一种插值技术。本文的主要贡献在于，我们表明：尽管缺乏指数可镇定性，仍可定义一个适定的 LQR 问题，并能够实施一种基于 Riccati 的方法来设计反馈控制。
英文摘要：
This paper studies an infinite time horizon LQR optimal control problem for a system describing, within a linear approximation, the vertical oscillations of a floating solid, coupled to the motion of the free boundary fluid on which it floats. The fluid flow is described by a viscous version of the linearized Saint-Venant equations (shallow water regime). The major difficulty we are facing is that the domain occupied by the fluid is unbounded so that the system is not exponentially stable. This fact firstly raises challenges in proving the wellposedness, requiring the combined use of analytic semigroup theory and of an interpolation technique. The main contribution of the paper is that we show that, in spite of the lack of exponential stabilizability, we can define a wellposed LQR problem for which a Riccati based approach to design feedback controls can be implemented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
