权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Research of "Algebraic and analytic methods in the spectrum for boundary control systems and numerical analysis"

“边界控制系统谱中的代数和解析方法及数值分析”研究

基本信息

批准号：
15540205
负责人：
NAMBU Takao
金额：
$ 1.47万
依托单位：
Kobe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540205/
关键词：
static feedback control scheme internal singularity parabolic boundary control systems boundary stabilization Klein-Gordon equations self-similar solutions self-referential agent-based model dynamic compensator removement of internal struc

项目摘要

1.(Nambu) Stabilization of linear parabolic systems in static feedback scheme is studied : When both the sensors and the actuators have spillovers, the stabilization problem is extremely difficult. By investigating the property of the fundamental solution to the finite-dimensional substructure and introducing a small parameter γ > 0, the stabilization is achieved as long as both the observability and the controllability assumptions are fulfilled and γ is small. When the dimension n of the substructure increases, it is shown that the internal singularity in γ increases. However, this singularity can be removed if n 【less than or equal】 5. This result is reported in the "7th-floor seminar, Waseda University", 2005.2.(Nambu) Stabilization of linear parabolic systems in dynamic feedback scheme is studied : It is shown that the well known analytic approach via fractional powers of the associated elliptic operator is no more applied to a variety of complicated boundary control systems. As an … More alternative, an entirely new algebraic transform working in the standard L^2-spaces is introduced. Via a finite-dimensional dynamic compensator of general type, a unified stabilization scheme is developed and achieved for general control systems with more complicated boundary conditions.3.(Nambu) In regular state stabilization problems the necessary number of the sensors and the actuators is at least the maximum of the multiplicities for the unstable eigenvalues. When the number is smaller than the required one and thus the observability and the controllability conditions are lost, it is shown that at least the output stabilization can be achieved by suitably constructing the feedback scheme.4.(Nakagiri) In the problem of parameter estimation for nonlinear hyperbolic systems, a characterization of the estimated solutions is achieved. A uniqueness condition between solutions and inputs is obtained in retarded functional differential equations. A related numerical computation for the perturbed Klein-Gordon equation is studied.5.(Nakagiri) Optimal control problems are studied for semilinear evolution equations of 2nd order, such as sine-Gordon equations and Klein-Gordon equations.6.(Tabata) In the macro analysis of mathematical economy, two self-referential agent-based models are studied and compared with each other. Sufficient conditions are obtained for existence and non-existence of scaling limits. In the agent-based model describing the population dynamics such as the recent change of labor dynamics in European Continent, it is shown that the model asymptotically approaches to the steady state (probabilistic density convergence).7.(Naito) The structure of self-similar solutions to a class of semilinear heat conduction equations is studied. The existence of the minimum positive solutions is shown via the super solution-sub solution method in the related nonlinear elliptic problem. In boundary value problems of o. d. equations with a class of subcritical nonlinear terms, the existence of multiple solutions is also shown. Less

1.研究了线性抛物型系统在静态反馈控制下的镇定问题：当传感器和执行器都存在溢出时，镇定问题是极其困难的。通过研究有限维子结构基本解的性质，引入一个小参数γ > 0，只要满足能观性和能控性假设，且γ很小，就可以实现系统的镇定.当子结构的维数n增加时，γ中的内部奇异性增加。然而，如果n [小于或等于] 5，则可以去除该奇异性。这一结果发表在早稻田大学第7层研讨会上，2005年2月。本文研究了线性抛物型系统在动态反馈控制下的镇定问题，证明了著名的椭圆算子分数幂解析方法不再适用于各种复杂的边界控制系统。作为 ...更多信息另一种方法是引入一种在标准L^2-空间中工作的全新代数变换。通过一个一般类型的有限维动态补偿器，对于具有更复杂边界条件的一般控制系统，得到了一个统一的镇定方案.（Nambu）在正则状态镇定问题中，传感器和执行器的必要数量至少是不稳定特征值的重数的最大值。结果表明，当系统的可观测性和可控制性条件丧失时，通过适当地构造反馈方案，至少可以实现输出镇定.（Nakagiri）在非线性双曲型系统的参数估计问题中，获得了估计解的特征。得到了时滞泛函微分方程解与输入之间的唯一性条件。研究了扰动Klein-Gordon方程的相关数值计算.研究了二阶半线性发展方程，如sine-Gordon方程和Klein-Gordon方程的最优控制问题.在数理经济的宏观分析中，研究了两种基于自参照主体的模型，并进行了比较。得到了标度极限存在和不存在的充分条件。在描述人口动态（如欧洲大陆劳动力动态的近期变化）的基于主体的模型中，证明了模型渐近地接近于稳态（概率密度收敛）.研究了一类半线性热传导方程的自相似解的结构。利用上下解方法证明了相关非线性椭圆型方程最小正解的存在性。在边值问题中，D.方程的多个解的存在性。少