论文标题
带有无限运算符系数的Riccati方程的唯一性
Uniqueness for Riccati equations with unbounded operator coefficients
论文作者
论文摘要
在本文中，我们解决了差异和代数操作员riccati方程的唯一性问题，这是在其无限系数上的独特假设下。以这些假设为特征的边界控制系统类别涵盖了各种重要的物理相互作用，这些相互作用都是由耦合双曲线/抛物线偏微分方程的系统建模的。唯一性的证据提供了铲球并克服了复合动力学的特殊规律性特性所产生的障碍。这些结果补充了作者与Lasiecka共同设计的有限和无限时间范围线性季度问题的理论，作为Riccati方程的独特解决方案，进入了最佳控制的封闭环形式。
In this article we address the issue of uniqueness for differential and algebraic operator Riccati equations, under a distinctive set of assumptions on their unbounded coefficients. The class of boundary control systems characterized by these assumptions encompasses diverse significant physical interactions, all modeled by systems of coupled hyperbolic/parabolic partial differential equations. The proofs of uniqueness provided tackle and overcome the obstacles raised by the peculiar regularity properties of the composite dynamics. These results supplement the theories of the finite and infinite time horizon linear-quadratic problem devised by the authors jointly with Lasiecka, as the unique solution to the Riccati equation enters the closed loop form of the optimal control.
