Optimal bilinear control of a reparable multi-state system
Optimal bilinear control of a reparable multi-state system
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DOI：
10.1080/00207179.2020.1825819
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发表时间：
2020-09
影响因子：
2.1
通讯作者：
Weiwei Hu;Jun Liu
中科院分区：
文献类型：
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作者：
Weiwei Hu;Jun Liu
这项工作解决了一个最优双线性控制设计，代表了一个可修复的多状态系统的纠正维护。主要的兴趣是优化系统的可用性，这被定义为系统在被请求使用时正常运行的概率。在我们目前的工作中考虑的系统模型是由耦合输运和积分微分方程控制的。纠正性维护策略由维修率表示，维修率取决于分布式维修时间。目标是确定在给定的系统运行周期内使系统在良好模式下的可用性最大化的最佳修复率。这本质上导致了一个双线性控制问题集在非自反巴拿赫空间使用-优化。给出了最优控制器存在性的严格证明和最优性的一阶必要条件。数值实验验证了理论结果。
This work addresses an optimal bilinear control design representing the corrective maintenance for a reparable multi-state system. The primary interest is to optimise the availability of the system, which is defined as the probability that the system is operating properly when it is requested for use. The system model considered in our current work is governed by coupled transport and integro-differential equations. A corrective maintenance policy is represented by the repair rate, which depends on the distributed repair time. The objective is to determine an optimal repair rate that maximises the availability of the system in good mode over a given system running period. This essentially leads to a bilinear control problem set in a nonreflexive Banach space using -optimisation. A rigorous proof of existence of an optimal controller and the first-order necessary conditions of optimality are addressed. Numerical experiments are conducted to demonstrate the theoretical results.