SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

MAXIMAL ELEMENTS OF A FAMILY OF G_B-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS

A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces （in short, FC-space） involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.

Coincidence Point Theorems,Intersection Theorems and Saddle Point Theorems on FC-spaces

In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.

GENERALIZED VECTOR VARIATIONAL-TYPE INEQUALITIES IN FC-SPACES

A class of generalized vector variational-type inequality problems （GVVTIP） are studied in FC-spaces, which includes the most of vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems and general- ized vector variational inequality problem as special cases. By using F-KKM theorem, some new existence results for GVVTIP axe established in noncompact FC-space. As consequences, some recent known results in literature are obtained under much weaker assumption.

ON COLLECTIVELY FIXED POINT THEOREMS ON FC-SPACES

Based on a KKM type theorem on FC-space, some new fixed point theorems for Fan-Browder type are established, and then some collectively fixed point theorems for a family of Ф-maps defined on product space of FC-spaces are given.These results generalize and improve many corresponding results.

Systems of generalized quasi-variational inclusion (disclusion) problems in FC-spaces

By applying an existence theorem of maximal elements of set-valued mappings in FC-spaces proposed by the author, some new existence theorems of solutions for systems of generalized quasi-variational inclusion （disclusion） problems are proved in FC-spaces without convexity structures. These results improve and generalize some results in recent publications from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions.

KKM Theorems on FC-spaces with Their Applications to Variational Inequalities

A new concept of finitely continuous topological spaces （in short, FC-space） without convexity structure and linear structure was introduced. Some KKM type theorems in noncompact FC-spaces were obtained, and from which, some section theorems and wriational inequality theorems were proved under much weak assumptions. Our results improve and generalize the corresponding conclusions in recent literature.

Generalized S-KKM Theorems and Minimax Inequalities in FC-Spaces

The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.

System of Generalized Vector Quasi-Equilibrium Problems in Locally FC-Spaces

A new class of locally finite continuous topological spaces （for short, locally FC-spaces） and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures.

Coincidence Theorem for Admissible Set-valued Mappings and Its Applications in FC-spaces

A new coincidence theorem for admissible set-valued mappings is proved in FC-spaces with a more general convexity structure. As applications, an abstract variational inequality, a KKM type theorem and a fixed point theorem are obtained. Our results generalize and improve the corresponding results in the literature.

基于拓展控制集的PMSM有限控制集无模型预测电流控制策略

永磁同步电机(permanent magnet synchronous motor,PMSM)具有高效率、高功率密度与高可靠性等优势,已在工业界得到广泛应用。文中针对PMSM驱动系统,提出基于拓展控制集的有限控制集无模型预测电流控制(finite-control-set model-free predictive current control,FCS-MFPCC)。首先,分析PMSM系统的数学模型并详述有限控制集模型预测电流控制(finite-control-set model predictive current control,FCS-MPCC)的原理。其次,介绍基于线性扩张状态观测器(linear extended state observer,LESO)的传统FCS-MFPCC。针对传统FCS-MFPCC稳态性能不足的问题,采用基于离散空间矢量调制(discrete space vector modulation,DSVM)的控制集拓展方案,将控制集的电压矢量数目拓展至25。然后,为解决拓展控制集带来的高计算量问题,提出一种快速寻优策略,阐述该策略的实施原理与流程。最后,基于一台500 W PMSM实验平台,对比传统FCS-MFPCC与所提FCS-MFPCC的控制性能,验证所提算法的有效性与优越性。实验结果表明,所提算法能够有效提升系统稳态性能,且定子绕组电流总谐波畸变率由10.07%降低至6.48%。

基于V2G技术的电动汽车充放电系统拓扑结构及控制策略研究

车辆到电网(vehicle to grid, V2G)技术可实现电动汽车与电网能量双向互动,可减轻对电力系统的潜在负荷影响并且对电网起到“削峰填谷”的作用,以此提高供电可靠性。目前,V2G系统网侧电流谐波的抑制效果并不显著,为了降低谐波畸变率,设计了一种基于脉宽调制(pulse-width modulation, PWM)型整流器和双向DC-DC变换器的拓扑结构,用以控制网侧与蓄电池的能量流动;提出了一种充电和放电时分别采用电压电流双闭环控制以及有限集模型预测电流控制(finite-control-set model predictive current control, FCS-MPCC)的策略,更好地抑制网侧电流谐波,降低谐波畸变率。在Matlab/Simulink中搭建了V2G系统模型进行仿真验证,仿真结果表明设计的V2G系统可实现网侧与蓄电池的互动,充电状态下网侧电流总谐波畸变率降为0.33%,放电状态下网侧电流总谐波畸变率降为0.48%,有效解决了电动汽车并网导致的电流谐波畸变。

FC-空间中的交定理及其应用(英文)

在不具有任何凸结构的FC-空间中证明了一个新的交定理.做为应用,证明了一个不动点定理、一个极大元定理和一个叠合定理.

不动点定理在拟平衡问题组中的应用

在不具有任何凸性结构和线性结构的有限连续空间(简称,FC-空间)中引入了新的拟平衡问题组,并运用FC-空间中的不动点定理,证明了这些拟平衡问题组的平衡点的存在性.这些结果推广了近期文献在抽象凸空间中的一些重要的平衡问题和拟平衡问题的存在结果.

FC-空间上的相交定理及其应用

介绍了FC-空间的定义和该空间上的KKM映射,利用已有的FC-空间上的KKM定理得出相交定理,最后作为应用讨论了截口点的存在问题和变分不等式解的存在问题。

有限度量紧开值集值映射的R-KKM定理及其对不动点的应用

在非紧FC-度量空间中建立了有限度量紧开值集值映射的R-KKM定理.作为应用,获得了非紧FC-度量空间中有限度量紧开(闭)值集值映射的匹配定理、重合定理和不动点定理.

FC-空间中的KKM型定理和重合点定理在广义矢量平衡问题中的应用

在FC-空间中引入FC-KKM(X,Y)集值映象类,并在FC-空间中证明了一些新的KKM型定理和重合点定理,作为应用,证明了FC-空间中广义矢量平衡问题平衡点的存在定理.

局部FC-一致空间内的广义约束多目标对策

在没有任何凸性结构的局部FC-一致空间内引入和研究了一类新的广义约束多目标对策,其中局中人数可以是有限或无限的和所有的支付函数可以取值于无限维空间.利用在局部FC-一致空间内得到的一个Himmelberg型不动点定理,在局部FC-一致空间内对广义约束多目标对策建立了某些弱Pareto平衡存在性定理.这些定理改进,统一和推广了最近文献中相应结果.

一类抽象广义矢量平衡问题

在有限连续空间中建立了一些抽象广义矢量平衡问题,并利用拓扑空间中的广义R-KKM型定理和有限连续空间中的KKM型定理,讨论了这类平衡问题平衡点的存在性,同时这些定理把某些G-凸空间中的结论推广到了有限连续空间.