摘要
广义分布参数系统是比分布参数系统更常见的一类系统,二者有着本质的区别,如广义分布参数系统受到干扰时会旨起脉冲行为等.广义分布参数系统的可解性问题是广义分布参数系统研究的重要问题之一.本文主要研究Banach空间中时变广义分布参数系统的可解性问题.首先,讨论Banach空间中由有界线性算子所弓『导的广义发展算子及其性质,定义了广义发展算子的生成元,证明了广义发展算子的存在性;然后,应用广义发展算子研究时变广义分布参数系统的可解性问题,证明了强解的存在性和唯一性,并应用广义发展算子给出了时变广义分布参数系统强解的构造性表达式.所得结果对于研究时变广义分布参数系统的稳定性问题、能控性问题及最优控制问题等都有重要的理论及应用价值.
Singular distributed parameter systems are encountered much more often than distributed parameter systems. There is an essential distinction between singular and ordinary distributed parameter systems. A disturbance not only reduces the stability of singular distributed parameter systems but also strongly affects the structures of such systems, leading to, for example, impulsive behavior. Solvability is one of the most important problems in the study of singular distributed parameter systems. The main purpose of this paper is to study the solvability of a time-varying singular distributed parameter system in Banach space. First, the generalized evolution operator induced by a bounded linear operator is introduced in Banach space, the properties of the generalized evolution operator are discussed, the generator of the generalized evolution operator is defined, and the existence of a generalized evolution operator is proved; then the solvability of the time-varying singular distributed parameter system is discussed using the generalized evolution operator, the existence and uniqueness of the strong solution are proved, and a constructive expression of the strong solution of the time-varying singular distributed parameter system is obtained. This research is theoretically and practically important to the study of the stability, controllability, and optimal control problem of the time-varying singular distributed parameter system.
出处
《中国科学：信息科学》
CSCD
2013年第3期386-406,共21页
Scientia Sinica(Informationis)
基金
国家自然科学基金(批准号:61174081)资助项目
关键词
可解性
强解
时变广义分布参数系统
广义发展算子
BANACH空间
solvability, strong solution, time-varying singular distributed parameter system, generalized evolu-tion operator, Banach space
