This paper introduces the concept of hierarchical-control-based output synchronization of coexisting attractor networks. Within the new framework, each dynamic node is made passive at first utilizing intra-control aro...This paper introduces the concept of hierarchical-control-based output synchronization of coexisting attractor networks. Within the new framework, each dynamic node is made passive at first utilizing intra-control around its own arena. Then each dynamic node is viewed as one agent, and on account of that, the solution of output synchronization of coexisting attractor networks is transformed into a multi-agent consensus problem, which is made possible by virtue of local interaction between individual neighbours; this distributed working way of coordination is coined as inter-control, which is only specified by the topological structure of the network. Provided that the network is connected and balanced, the output synchronization would come true naturally via synergy between intra and inter-control actions, where the rightness is proved theoretically via convex composite Lyapunov functions. For completeness, several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme.展开更多
A numerical method is proposed to approach the Approximate Inertial Man-ifolds(AIMs)in unsteady incompressible Navier-Stokes equations,using multilevel fi-nite element method with hierarchical basis functions.Followin...A numerical method is proposed to approach the Approximate Inertial Man-ifolds(AIMs)in unsteady incompressible Navier-Stokes equations,using multilevel fi-nite element method with hierarchical basis functions.Following AIMS,the unknown variables,velocity and pressure in the governing equations,are divided into two com-ponents,namely low modes and high modes.Then,the couplings between low modes and high modes,which are not accounted by standard Galerkin method,are consid-ered by AIMs,to improve the accuracy of the numerical results.Further,the multilevel finite element method with hierarchical basis functions is introduced to approach low modes and high modes in an efficient way.As an example,the flow around airfoil NACA0012 at different angles of attack has been simulated by the method presented,and the comparisons show that there is a good agreement between the present method and experimental results.In particular,the proposed method takes less computing time than the traditional method.As a conclusion,the present method is efficient in numer-ical analysis of fluid dynamics,especially in computing time.展开更多
基金supported by the State Key Laboratory of Scientific&Engineering Computing, Chinese Academy of Sciencesthe National Natural Science Foundation of China (Grant No. 60850004)+4 种基金the Funds for Creative Research Talents of Henan Education Bureau, China (Grant No. 2009HASTIT021)the Natural Science Foundation of Henan Education Bureau, China(Grant No. 2008A120005)Fundamental&Frontier Technology Research Planning Project of Henan Province,China (Grant No.072300460050)Doctoral Program of Henan Polytechnic University (Grant No. 648606)Young Teacher Key Talents Program of Henan Polytechnic University (Grant No. 649033)
文摘This paper introduces the concept of hierarchical-control-based output synchronization of coexisting attractor networks. Within the new framework, each dynamic node is made passive at first utilizing intra-control around its own arena. Then each dynamic node is viewed as one agent, and on account of that, the solution of output synchronization of coexisting attractor networks is transformed into a multi-agent consensus problem, which is made possible by virtue of local interaction between individual neighbours; this distributed working way of coordination is coined as inter-control, which is only specified by the topological structure of the network. Provided that the network is connected and balanced, the output synchronization would come true naturally via synergy between intra and inter-control actions, where the rightness is proved theoretically via convex composite Lyapunov functions. For completeness, several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme.
基金The research is supported by the National Basic Research Program of China(973 Program,Grant No.2012CB026002)the National Natural Science Foun-dation of China(Grant No.51305355).
文摘A numerical method is proposed to approach the Approximate Inertial Man-ifolds(AIMs)in unsteady incompressible Navier-Stokes equations,using multilevel fi-nite element method with hierarchical basis functions.Following AIMS,the unknown variables,velocity and pressure in the governing equations,are divided into two com-ponents,namely low modes and high modes.Then,the couplings between low modes and high modes,which are not accounted by standard Galerkin method,are consid-ered by AIMs,to improve the accuracy of the numerical results.Further,the multilevel finite element method with hierarchical basis functions is introduced to approach low modes and high modes in an efficient way.As an example,the flow around airfoil NACA0012 at different angles of attack has been simulated by the method presented,and the comparisons show that there is a good agreement between the present method and experimental results.In particular,the proposed method takes less computing time than the traditional method.As a conclusion,the present method is efficient in numer-ical analysis of fluid dynamics,especially in computing time.
