修理工可休假的退化可修复系统动态解的研究

修理工可休假的退化可修复系统是可靠性理论和应用中的重要系统,近年来许多学者研究修理工可休假的退化可修复系统的可靠性。本项目重点对各类修理工可休假的退化可修复系统进行深入的研究，研究系统的适定性、非负动态解的存在唯一性、稳态解的存在性、动态解的渐近稳定性和动态解的指数稳定性。进一步研究退化系统的最优控制问题,并利用数值计算和数值模拟的方法对本项目所得部分理论结果进行数值实验。这对退化可修复系统的可靠性有非常重要的科学意义。本项目的目标是建立各类退化可修复系统的适定性、动态解的存在性、动态解的渐近稳定性和动态解指数稳定性的简单、合理、并且易于验证的判别准则，从事这方面的研究工作的科研人员提供理论框架和方法。

Deteriorating repairable systems with vacation of repairman have been studied by many researchers in recent year due to their importance in in reliability theory and applications. In this project, we focus on the various types of deteriorating repairable systems attended by a repairman with vacation, we will study the well-posedness, the existence and uniqueness of the nonnegative dynamic solution, the existence of the steady state solution and the asymptotic stability as well as the exponential stability of the systems. Furthermore,we study the problem of optimal control of the systems, and by using the numerical calculation and the numerical simulation method, we execute numerical periments on some theoretical results obtained in this project, which are very important scientific significance in the reliability of the deteriorating systems. Main goal of this project is to build a simple and reasonable criterion for studying well-posedness, the existence and uniqueness of the dynamic solution, and the asymptotic stability as well as the exponential stability of various types of deteriorating repairable systems, and to provide a theoretical framework and methodology to the researchers in this area.