设 G=(V,E)是简单图,n 是任意正整数,用γ_n(G)γ_n^l(G),i_n(G)和iγ_n(G)分别表示 G 的 n-控制数、全 n-控制数、独立 n-控制数和 n-无赘数。本文得到的结果为(i)γ_n^l(G)≤2iγ_n(G);(ii)如果 G 中存在一个具有 k 个 n-孤立点的 iγ...设 G=(V,E)是简单图,n 是任意正整数,用γ_n(G)γ_n^l(G),i_n(G)和iγ_n(G)分别表示 G 的 n-控制数、全 n-控制数、独立 n-控制数和 n-无赘数。本文得到的结果为(i)γ_n^l(G)≤2iγ_n(G);(ii)如果 G 中存在一个具有 k 个 n-孤立点的 iγ_n(G)—集,则γ_n(G)≤2iγ_n(G)-(k+1),上述此不等式推广了 Allan 等在文献[1]中的结论。展开更多
For a positive integer k,the total{k}-dominating function(T{k}DF)of a graph G without isolated vertices is a function f from the vertex set V(G)to the set{0,1,2,…,k}such that for each vertex v∈V(G),the sum of the va...For a positive integer k,the total{k}-dominating function(T{k}DF)of a graph G without isolated vertices is a function f from the vertex set V(G)to the set{0,1,2,…,k}such that for each vertex v∈V(G),the sum of the values of all its neighbors assigned by f is at least k.A set{f_(1),f_(2),…,f_(d)}of pairwise different T{k}DF s of G with the property that∑d i=1 f_(i)(v)≤k for each v∈V(G),is called a total{k}-dominating family(T{k}D family)of G.The total{k}-domatic number of a graph G,denoted by d^({k})_(t)(G),is the maximum number of functions in T{k}D family.In 2013,Aram et al.proposed a problem that whether or not d^({k})_(t)(C_(m)□C_(n))=3 when 4 nmk,and d^({k})_(t)(C m□C n)=4 when 4|nmk.It was shown that d^({k})_(t)(C_(m)□C_(n))=3 if 4 nmk and k≥2 or 4|nmk and 2 nk,which partially answered the above problem.In addition,the total{k}-domatic number of the direct product of a cycle and a path,two paths,and two cycles was studied,respectively.展开更多
A nonlinear robust control strategy is proposed to force an underactuated surface ship to follow a predefined path with uncertain environmental disturbance and parameters.In the controller design,a high-gain observer ...A nonlinear robust control strategy is proposed to force an underactuated surface ship to follow a predefined path with uncertain environmental disturbance and parameters.In the controller design,a high-gain observer is used to estimate velocities,thus only position and yaw angle measurements are required.The control problem of underactuated system is transformed into a control of fully actuated system through adopting an improved line-of-sight(LOS) guidance law.A sliding-mode controller is designed to eliminate the yaw angle error,and provide the control system robustness.The control law is proved semi-globally exponentially stable(SGES) by applying Lyapunov stability theory,and numerical simulation using real data of a monohull ship illustrates the effectiveness and robustness of the proposed methodology.展开更多
Plenty of dams in China are in danger while there are few effective methods for underwater dam inspections of hidden problems such as conduits,cracks and inanitions.The dam safety inspection remotely operated vehicle(...Plenty of dams in China are in danger while there are few effective methods for underwater dam inspections of hidden problems such as conduits,cracks and inanitions.The dam safety inspection remotely operated vehicle(DSIROV) is designed to solve these problems which can be equipped with many advanced sensors such as acoustical,optical and electrical sensors for underwater dam inspection.A least-square parameter estimation method is utilized to estimate the hydrodynamic coefficients of DSIROV,and a four degree-of-freedom(DOF) simulation system is constructed.The architecture of DSIROV's motion control system is introduced,which includes hardware and software structures.The hardware based on PC104 BUS,uses AMD ELAN520 as the controller's embedded CPU and all control modules work in VxWorks real-time operating system.Information flow of the motion system of DSIROV,automatic control of dam scanning and dead-reckoning algorithm for navigation are also discussed.The reliability of DSIROV's control system can be verified and the control system can fulfill the motion control mission because embankment checking can be demonstrated by the lake trials.展开更多
文摘设 G=(V,E)是简单图,n 是任意正整数,用γ_n(G)γ_n^l(G),i_n(G)和iγ_n(G)分别表示 G 的 n-控制数、全 n-控制数、独立 n-控制数和 n-无赘数。本文得到的结果为(i)γ_n^l(G)≤2iγ_n(G);(ii)如果 G 中存在一个具有 k 个 n-孤立点的 iγ_n(G)—集,则γ_n(G)≤2iγ_n(G)-(k+1),上述此不等式推广了 Allan 等在文献[1]中的结论。
基金supported by NSFSD(No.BS2010SF017,Y2008A04)NNSFC(No.11101245)+1 种基金Foundation of Education Committee of Shandong Province(J07YH03)Foundation of Shandong Institute of Business and Technology(2011QF073)
基金Supported by NNSF of China(11671376,11401004)Anhui Provincial Natural Science Foundation(1708085MA18)
文摘For a positive integer k,the total{k}-dominating function(T{k}DF)of a graph G without isolated vertices is a function f from the vertex set V(G)to the set{0,1,2,…,k}such that for each vertex v∈V(G),the sum of the values of all its neighbors assigned by f is at least k.A set{f_(1),f_(2),…,f_(d)}of pairwise different T{k}DF s of G with the property that∑d i=1 f_(i)(v)≤k for each v∈V(G),is called a total{k}-dominating family(T{k}D family)of G.The total{k}-domatic number of a graph G,denoted by d^({k})_(t)(G),is the maximum number of functions in T{k}D family.In 2013,Aram et al.proposed a problem that whether or not d^({k})_(t)(C_(m)□C_(n))=3 when 4 nmk,and d^({k})_(t)(C m□C n)=4 when 4|nmk.It was shown that d^({k})_(t)(C_(m)□C_(n))=3 if 4 nmk and k≥2 or 4|nmk and 2 nk,which partially answered the above problem.In addition,the total{k}-domatic number of the direct product of a cycle and a path,two paths,and two cycles was studied,respectively.
基金Projects(61004008,51509055)supported by the National Natural Science Foundation of ChinaProject(61422230302162223013)supported by the Laboratory of Science and Technology on Water Jet Propulsion,China
文摘A nonlinear robust control strategy is proposed to force an underactuated surface ship to follow a predefined path with uncertain environmental disturbance and parameters.In the controller design,a high-gain observer is used to estimate velocities,thus only position and yaw angle measurements are required.The control problem of underactuated system is transformed into a control of fully actuated system through adopting an improved line-of-sight(LOS) guidance law.A sliding-mode controller is designed to eliminate the yaw angle error,and provide the control system robustness.The control law is proved semi-globally exponentially stable(SGES) by applying Lyapunov stability theory,and numerical simulation using real data of a monohull ship illustrates the effectiveness and robustness of the proposed methodology.
基金Project(20100480964) supported by China Postdoctoral Science FoundationProjects(2002AA420090,2008AA092301) supported by the National High Technology Research and Development Program of China
文摘Plenty of dams in China are in danger while there are few effective methods for underwater dam inspections of hidden problems such as conduits,cracks and inanitions.The dam safety inspection remotely operated vehicle(DSIROV) is designed to solve these problems which can be equipped with many advanced sensors such as acoustical,optical and electrical sensors for underwater dam inspection.A least-square parameter estimation method is utilized to estimate the hydrodynamic coefficients of DSIROV,and a four degree-of-freedom(DOF) simulation system is constructed.The architecture of DSIROV's motion control system is introduced,which includes hardware and software structures.The hardware based on PC104 BUS,uses AMD ELAN520 as the controller's embedded CPU and all control modules work in VxWorks real-time operating system.Information flow of the motion system of DSIROV,automatic control of dam scanning and dead-reckoning algorithm for navigation are also discussed.The reliability of DSIROV's control system can be verified and the control system can fulfill the motion control mission because embankment checking can be demonstrated by the lake trials.
