强耦合抛物型系统中主耦合消失时的尖锐可观测性代价
Sharp Observability Costs for Strongly Coupled Parabolic Systems with Vanishing Principal Coupling
浏览论文内容
中文总结 AI 辅助
本文研究强耦合抛物系统在耦合参数趋于零时的可观测性代价，在Kalman秩条件下确定了精确的爆破速率，并证明零控制的最小L∞范数具有相同渐近行为。
中文摘要 AI 辅助
我们研究一类强耦合抛物型系统在耦合参数趋于零时的可观测性损失。该系统通过一个固定的矩阵 $B$ 在时空的正测度可测子集上被观测。在 Kalman 秩条件下，我们确定了最优可观测性代价的精确爆破速率。状态的不同分量以及它们的不同组合可能具有不同的爆破速率，这些速率由对 $(B,K)$ 的代数结构决定。全状态可观测性代价由这些速率中的最大值决定。我们还证明了零控制的最坏情形最小 $L^\infty$ 范数具有相同的渐近行为。
英文摘要
We study the loss of observability for a class of strongly coupled parabolic systems as the coupling parameter tends to zero. The system is observed through a fixed matrix $B$ on a measurable subset of space-time with positive measure. Under the Kalman rank condition, we determine the exact blow-up rates of the optimal observability cost. Different components of the state, as well as different combinations of them, may have different blow-up rates, and these rates are determined by the algebraic structure of the pair $(B,K)$. The full-state observability cost is determined by the largest of these rates. We also show that the worst-case minimum $L^\infty$-norm of null controls has the same asymptotic behavior.
发表机构
- Civil Aviation Flight University of China（中国民航飞行学院）
机构由 AI 辅助整理，请以论文原文为准。
