The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzz...The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.展开更多
This paper proposes a new matrix product, namely, semi-tensor product. It is a general-ization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The p...This paper proposes a new matrix product, namely, semi-tensor product. It is a general-ization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The purpose of introducing this product is twofold: (i) treat multi-dimensional da-ta; (ii) treat nonlinear problems in a linear way. Then the computer and numerical methods can be easily used for solving nonlinear problems. Properties and formulas are deduced. As an application, the Morgan's problem for control systems is formulated as a numerically solvable problem.展开更多
The reachability problem of synchronizing transitions bounded Petri net systems （BPNSs） is investigated in this paper by constructing a mathematical model for dynamics of BPNS. Using the semi-tensor product （STP） ...The reachability problem of synchronizing transitions bounded Petri net systems （BPNSs） is investigated in this paper by constructing a mathematical model for dynamics of BPNS. Using the semi-tensor product （STP） of matrices, the dynamics of BPNSs, which can be viewed as a combination of several small bounded subnets via synchronizing transitions, are described by an algebraic equation. When the algebraic form for its dynamics is established, we can present a necessary and sufficient condition for the reachability between any marking （or state） and initial marking. Also, we give a corresponding algorithm to calculate all of the transition paths between initial marking and any target marking. Finally, an example is shown to illustrate proposed results. The key advantage of our approach, in which the set of reachable markings of BPNSs can be expressed by the set of reachable markings of subnets such that the big reachability set of BPNSs do not need generate, is partly avoid the state explosion problem of Petri nets （PNs）.展开更多
随着工业4.0的发展,移动智能体系统(Mobile agent system,MAS)与多回路无线控制系统(Wireless control system,WCS)被部署到工厂中,构成异构工业物联网(Industrial internet of things,IIoT)系统,协作执行智能制造任务.在协作过程中,MAS...随着工业4.0的发展,移动智能体系统(Mobile agent system,MAS)与多回路无线控制系统(Wireless control system,WCS)被部署到工厂中,构成异构工业物联网(Industrial internet of things,IIoT)系统,协作执行智能制造任务.在协作过程中,MAS与WCS紧密耦合,导致状态相关衰落,两者性能相互制约.为解决这一问题,研究异构工业物联网系统的最优控制问题,满足WCS控制性能约束与MAS安全生产约束的同时,最小化系统平均通信成本.首先,利用有限域系统描述MAS在不同阴影衰落程度工作区间的转移,刻画MAS与WCS耦合下的状态相关衰落信道模型.基于此,利用矩阵半张量积理论,通过构建受限跟随者状态转移图(Follower state transition graph,FSTG),建立最优控制问题可行性图判据,给出关于受限集合镇定的充分必要条件.其次,基于加权跟随者状态转移图的最小平均环理论,建立领航-跟随MAS最优控制序列的构造算法,并证明其最优性.最后,通过仿真验证算法的有效性.展开更多
In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, wh...In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.展开更多
基金This work was partially supported by the Natural Science Foundation of China （No. 611 74094） the Tianjin Natural Science Foundation of China （No. 13JCYBJC1 7400） the Program for New Century Excellent Talents in University of China （No. NCET-10-0506）.
文摘The problem of solving type-2 fuzzy relation equations is investigated. In order to apply semi-tensor product of matrices, a new matrix analysis method and tool, to solve type-2 fuzzy relation equations, a type-2 fuzzy relation is decomposed into two parts as principal sub-matrices and secondary sub-matrices; an r-ary symmetrical-valued type-2 fuzzy relation model and its corresponding symmetrical-valued type-2 fuzzy relation equation model are established. Then, two algorithms are developed for solving type-2 fuzzy relation equations, one of which gives a theoretical description for general type-2 fuzzy relation equations; the other one can find all the solutions to the symmetrical-valued ones. The results can improve designing type-2 fuzzy controllers, because it provides knowledge to search the optimal solutions or to find the reason if there is no solution. Finally some numerical examples verify the correctness of the results/algorithms.
基金This work was supported by the National Natural Science Foundation of China ( Grant Nos. G69774008, G59837270) National 973 Project (Grant No. G1998020308) National Key Project of China.
文摘This paper proposes a new matrix product, namely, semi-tensor product. It is a general-ization of the conventional matrix product. Meanwhile, it is also closely related to Kronecker (tensor) product of matrices. The purpose of introducing this product is twofold: (i) treat multi-dimensional da-ta; (ii) treat nonlinear problems in a linear way. Then the computer and numerical methods can be easily used for solving nonlinear problems. Properties and formulas are deduced. As an application, the Morgan's problem for control systems is formulated as a numerically solvable problem.
基金supported by the National Natural Science Foundation of China(61573199,61573200)the Tianjin Natural Science Foundation(14JCYBJC18700)
文摘The reachability problem of synchronizing transitions bounded Petri net systems （BPNSs） is investigated in this paper by constructing a mathematical model for dynamics of BPNS. Using the semi-tensor product （STP） of matrices, the dynamics of BPNSs, which can be viewed as a combination of several small bounded subnets via synchronizing transitions, are described by an algebraic equation. When the algebraic form for its dynamics is established, we can present a necessary and sufficient condition for the reachability between any marking （or state） and initial marking. Also, we give a corresponding algorithm to calculate all of the transition paths between initial marking and any target marking. Finally, an example is shown to illustrate proposed results. The key advantage of our approach, in which the set of reachable markings of BPNSs can be expressed by the set of reachable markings of subnets such that the big reachability set of BPNSs do not need generate, is partly avoid the state explosion problem of Petri nets （PNs）.
文摘随着工业4.0的发展,移动智能体系统(Mobile agent system,MAS)与多回路无线控制系统(Wireless control system,WCS)被部署到工厂中,构成异构工业物联网(Industrial internet of things,IIoT)系统,协作执行智能制造任务.在协作过程中,MAS与WCS紧密耦合,导致状态相关衰落,两者性能相互制约.为解决这一问题,研究异构工业物联网系统的最优控制问题,满足WCS控制性能约束与MAS安全生产约束的同时,最小化系统平均通信成本.首先,利用有限域系统描述MAS在不同阴影衰落程度工作区间的转移,刻画MAS与WCS耦合下的状态相关衰落信道模型.基于此,利用矩阵半张量积理论,通过构建受限跟随者状态转移图(Follower state transition graph,FSTG),建立最优控制问题可行性图判据,给出关于受限集合镇定的充分必要条件.其次,基于加权跟随者状态转移图的最小平均环理论,建立领航-跟随MAS最优控制序列的构造算法,并证明其最优性.最后,通过仿真验证算法的有效性.
基金This work was partially supported by National Natural Science Foundation of China （Nos. 61273013, 61333001, 61104065, 61322307）.
文摘In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.
基金supported by the National Natural Science Foundation of China(Nos.G61074068,G61034007,G61174036,G61374065)the Research Fund for the Taishan Scholar Project of Shandong Province of Chinathe Scholarship Award for Excellent Doctoral Student granted by Ministry of Education
