具有退化状态的可修复系统的适定性与双线性能控性
Well-posedness and Bilinear Controllability of a Repairable System with Degraded State
AI总结：
本文研究含正常、退化与故障三状态的可修复输运系统，证明有限最大修复时间下的适定性与渐近行为，并设计时空修复策略实现双线性能控以提升可用性。
摘要：
在本工作中，我们考虑以三种不同状态为特征的可修复系统动力学：一种表示正常运行状态，另一种表示退化状况，第三种表示故障状况。这些系统的特点是在发生故障和/或退化时能够被修复。这类系统通常由输运方程描述，表现出耦合性质，通过积分-微分方程和积分边界条件相互联系，这些方程支配所有状态之间的转移。在本文中，我们处理两个较少被探索的方面：1）最大修复时间有限时此类系统的适定性和渐近行为；2）通过修复作用实现系统的双线性能控性。特别地，我们聚焦于仅存在一个退化状态和一个故障状态的情形。我们首先针对给定的与时间无关的修复率讨论第1）部分，随后设计依赖于空间-时间的修复策略，这些策略能够在有限时域内操纵系统动力学以达到期望水平。我们的目标是提高系统可用性——即在固定时间段内需要系统时其处于可运行状态的概率。我们给出严格分析，并开发利用系统模型双线性结构的控制策略。
英文摘要：
In this work, we consider the dynamics of repairable systems characterized by three distinct states: one signifying normal operational states, another representing degraded conditions and a third denoting failed conditions. These systems are characterized by their ability to be repaired when failures and/or degradation occur. Typically described by transport equations, these systems exhibit a coupled nature, interlinked through integro-differential equations and integral boundary conditions that dictate the transitions among all the states. In this paper, we address two less-explored facets: 1) the well-posedness and the asymptotic behavior of such systems with maximum repair time being finite; and 2) the bilinear controllability of the system via repair actions. In particular, we focus on the case where only one degraded and one failed states exist. We first discuss part 1) for given time-independent repair rates and then design the space-time dependent repair strategies that can manipulate system dynamics to achieve the desired level over a finite horizon. Our objective is to enhance the system availability -- the probability of being operational when needed over a fixed period of time. We present rigorous analysis and develop control strategies that leverage the bilinear structure of the system model.
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。
