Banach空间中不适定线性算子的广义概率范数  

The Norm of Generalized Probability of Ilt-posed Linear Operators in Banach Spaces

作　　者：江慧敏 JIANG Huimin(Wannan Medical College,Wuhu 241000,China)

机构地区：[1]皖南医学院

出　　处：《安阳师范学院学报》2019年第5期1-4,7,共5页Journal of Anyang Normal University

摘　　要：Banach空间中不适定线性算子的稳定性决定非线性系统的鲁棒性,分析Banach空间中不适定线性算子的广义概率范数,构建概率拟合模型,在给定的约束泛函下,采用Lyapunov-Krasovskii差分进化方法进行Banach空间中不适定线性算子的输出稳定特征解分析,构建Banach空间中不适定线性系统的定量递归分析模型;结合二次非线性波动演化博弈方法,实现对不适定线性算子的广义概率稳定特征解自适应寻优;结合正态分布模型、正态对数分布模型和Weibull分布模型,实现对Banach空间中不适定线性算子的广义概率范数分析,提高输出稳定性。数学推导结果表明,Banach空间中不适定线性算子具有稳定解,广义概率范数是稳态收敛的。The stability of ill-posed linear operators in Banach spaces determines the robustness of nonlinear systems.The generalized probability norm of ill-posed linear operators in Banach spaces is analyzed,and the probability fitting model is constructed to analyze the stability characteristics of ill-posed linear operators in Banach spaces.Under the given constraint functional,the Lyapunov-Krasovskii difference evolution method is used to analyze the output stability characteristic solutions of ill-posed linear operators in Banach spaces.The quantitative recurrent analysis model of ill-posed linear systems in Banach spaces is constructed.The constrained control method is used to analyze the quantitative characteristics of generalized probability norm.Combined with the quadratic nonlinear wave evolution game method,the adaptive optimization of the generalized probabilistic stability characteristic solution of ill-posed linear operators is realized,combined with the normal distribution model,the normal logarithmic distribution model and the Weibull distribution model.The generalized probability norm analysis of ill-posed linear operators in Banach spaces is realized to improve the output stability.The mathematical derivation results show that the ill-posed linear operator in Banach spaces has stable solution and the generalized probability norm is steady-state convergence.

关 键 词：BANACH空间 不适定线性算子 广义概率范数 稳定解 

分 类 号：O177.2[理学—数学]