Structural controllability is critical for operating and controlling large-scale complex networks. In real applications, for a given network, it is always desirable to have more selections for driver nodes which make ...Structural controllability is critical for operating and controlling large-scale complex networks. In real applications, for a given network, it is always desirable to have more selections for driver nodes which make the network structurally controllable. Different from the works in complex network field where structural controllability is often used to explore the emergence properties of complex networks at a macro level,in this paper, we investigate it for control design purpose at the application level and focus on describing and obtaining the solution space for all selections of driver nodes to guarantee structural controllability. In accord with practical applications,we define the complete selection rule set as the solution space which is composed of a series of selection rules expressed by intuitive algebraic forms. It explicitly indicates which nodes must be controlled and how many nodes need to be controlled in a node set and thus is particularly helpful for freely selecting driver nodes. Based on two algebraic criteria of structural controllability, we separately develop an input-connectivity algorithm and a relevancy algorithm to deduce selection rules for driver nodes. In order to reduce the computational complexity,we propose a pretreatment algorithm to reduce the scale of network's structural matrix efficiently, and a rearrangement algorithm to partition the matrix into several smaller ones. A general procedure is proposed to get the complete selection rule set for driver nodes which guarantee network's structural controllability. Simulation tests with efficiency analysis of the proposed algorithms are given and the result of applying the proposed procedure to some real networks is also shown, and these all indicate the validity of the proposed procedure.展开更多
Cellulose and its derivatives are natural materials with high carbon contents, but it is challenging to convert their carbon into high value-added carbonaceous materials(e.g., graphene). Here, an approach to convert t...Cellulose and its derivatives are natural materials with high carbon contents, but it is challenging to convert their carbon into high value-added carbonaceous materials(e.g., graphene). Here, an approach to convert the carbon in cellulose into N, P co-doped porous graphene(LIG) materials via laser induction is proposed. Cellulose nanofibrils(CNFs), a cellulose derivative with high dispersion uniformity and abundant surface hydroxyl groups, were easily formed on a bulk substrate(thickness ≥5 mm) containing ammonium polyphosphate(APP). Then, a 10.6 μm CO2 laser was used to scribe for 1–5 passes on the CNFs/APP substrate under an ambient environment to produce N, P co-doped porous LIG. Upon increasing the number of laser scribing passes, the IG/IDof LIG first increased and then decreased, reaching a maximum of 1.68 at 4 passes. The good pore structure and low resistance also showed that 4 laser passes were ideal. Besides, the N, P co-doped LIG also showed excellent electrochemical performance, with a specific capacitance of 221.4 FF·g^(-1) and capacitance retention of 89.9%. This method exploits the advantages of nanocellulose and overcomes the difficulties associated with directly compounding cellulosic materials, providing a method for the further development of biomass nanomaterials.展开更多
基金supported by the National Science Foundation of China(61333009,61473317,61433002,61521063,61590924,61673366)the National High Technology Research and Development Program of China(2015AA043102)
文摘Structural controllability is critical for operating and controlling large-scale complex networks. In real applications, for a given network, it is always desirable to have more selections for driver nodes which make the network structurally controllable. Different from the works in complex network field where structural controllability is often used to explore the emergence properties of complex networks at a macro level,in this paper, we investigate it for control design purpose at the application level and focus on describing and obtaining the solution space for all selections of driver nodes to guarantee structural controllability. In accord with practical applications,we define the complete selection rule set as the solution space which is composed of a series of selection rules expressed by intuitive algebraic forms. It explicitly indicates which nodes must be controlled and how many nodes need to be controlled in a node set and thus is particularly helpful for freely selecting driver nodes. Based on two algebraic criteria of structural controllability, we separately develop an input-connectivity algorithm and a relevancy algorithm to deduce selection rules for driver nodes. In order to reduce the computational complexity,we propose a pretreatment algorithm to reduce the scale of network's structural matrix efficiently, and a rearrangement algorithm to partition the matrix into several smaller ones. A general procedure is proposed to get the complete selection rule set for driver nodes which guarantee network's structural controllability. Simulation tests with efficiency analysis of the proposed algorithms are given and the result of applying the proposed procedure to some real networks is also shown, and these all indicate the validity of the proposed procedure.
基金supported by Beijing Zhongkebaice Technology Service Co.,Ltd.
文摘Cellulose and its derivatives are natural materials with high carbon contents, but it is challenging to convert their carbon into high value-added carbonaceous materials(e.g., graphene). Here, an approach to convert the carbon in cellulose into N, P co-doped porous graphene(LIG) materials via laser induction is proposed. Cellulose nanofibrils(CNFs), a cellulose derivative with high dispersion uniformity and abundant surface hydroxyl groups, were easily formed on a bulk substrate(thickness ≥5 mm) containing ammonium polyphosphate(APP). Then, a 10.6 μm CO2 laser was used to scribe for 1–5 passes on the CNFs/APP substrate under an ambient environment to produce N, P co-doped porous LIG. Upon increasing the number of laser scribing passes, the IG/IDof LIG first increased and then decreased, reaching a maximum of 1.68 at 4 passes. The good pore structure and low resistance also showed that 4 laser passes were ideal. Besides, the N, P co-doped LIG also showed excellent electrochemical performance, with a specific capacitance of 221.4 FF·g^(-1) and capacitance retention of 89.9%. This method exploits the advantages of nanocellulose and overcomes the difficulties associated with directly compounding cellulosic materials, providing a method for the further development of biomass nanomaterials.
