This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global ...This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global finite-time consensus for both single-integrator and double-integrator multi-agent systems with leaderless undirected and leader-following directed commu-nication topologies.These new protocols not only provide an explicit upper-bound estimate for the settling time,but also have a user-prescribed bounded control level.In addition,compared to some existing results based on the saturation function,the pro-posed approach considerably simplifies the protocol design and the stability analysis.Illustrative examples and an application demonstrate the effectiveness of the proposed protocols.展开更多
In this paper,we propose a second-order quasilinear hyperbolic system.By means of the theory on semi-global C^(1)solution to first-order quasilinear hyperbolic systems,we establish the existence and uniqueness of semi...In this paper,we propose a second-order quasilinear hyperbolic system.By means of the theory on semi-global C^(1)solution to first-order quasilinear hyperbolic systems,we establish the existence and uniqueness of semi-global C^(2)solution to this second-order quasilinear hyperbolic system.After then,the general constructive framework is utilized to obtain the local exact boundary controllability for this second-order system.展开更多
We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling fluid flows such as the blood flow through compliant axisyminetric vessels. Early models derived a...We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling fluid flows such as the blood flow through compliant axisyminetric vessels. Early models derived are nonconservative and/or nonho- mogeneous with measure source terms, which are endowed with infinitely many Riemann solutions for some Riemann data. In this paper, we derive a one-dimensional hyperbolic system that is conservative and homogeneous. Moreover, there exists a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data, under a natural stability entropy criterion. The Riemann solutions may consist of four waves for some cases. The system can also be written as a 3 × 3 system for which strict hyperbolicity fails and the standing waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue.展开更多
We obtain the Omori-Yau maximum principle on complete properly immersed submanifolds with the mean curvature satisfying certain condition in complete Riemannian manifolds whose radial sectional curvature satisfies som...We obtain the Omori-Yau maximum principle on complete properly immersed submanifolds with the mean curvature satisfying certain condition in complete Riemannian manifolds whose radial sectional curvature satisfies some decay condition, which generalizes our previous results in [17]. Using this generalized maximum principle, we give an estimate on the mean curvature of properly immersed submanifolds in H^n × R^e with the image under the projection on H^n contained in a horoball and the corresponding situation in hyperbolic space. We also give other applications of the generalized maximum principle.展开更多
In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the met...In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the metric spaces under certain condi- tions. As an application, for a group G strongly relatively hyperbolic to a subgroup H, the author proves that B（n） = {g ∈ G／ │g│suЭe≤ n} admits a coarse embedding into a uniformly convex Banach space if H does.展开更多
We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang...We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang’s previous result for modified asymptotically flat initial data sets.展开更多
For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the for...For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.展开更多
基金supported by the National Natural Science Foundation of China(62073019)。
文摘This paper investigates the problem of global/semi-global finite-time consensus for integrator-type multi-agent sys-tems.New hyperbolic tangent function-based protocols are pro-posed to achieve global and semi-global finite-time consensus for both single-integrator and double-integrator multi-agent systems with leaderless undirected and leader-following directed commu-nication topologies.These new protocols not only provide an explicit upper-bound estimate for the settling time,but also have a user-prescribed bounded control level.In addition,compared to some existing results based on the saturation function,the pro-posed approach considerably simplifies the protocol design and the stability analysis.Illustrative examples and an application demonstrate the effectiveness of the proposed protocols.
基金Supported by the Science and Technology Commission of Shanghai Municipality (Grant No.23ZR1402100)the Fundamental Research Funds for the Central Universities (Grant Nos. 2232022G-13 and 2232023G-13)
文摘In this paper,we propose a second-order quasilinear hyperbolic system.By means of the theory on semi-global C^(1)solution to first-order quasilinear hyperbolic systems,we establish the existence and uniqueness of semi-global C^(2)solution to this second-order quasilinear hyperbolic system.After then,the general constructive framework is utilized to obtain the local exact boundary controllability for this second-order system.
基金supported in part by the National Science Foundation under Grants DMS-0935967the National Science Foundation under Grants DMS-0807551+2 种基金the National Science Foundation under Grants DMS-0720925the National Science Foundation under Grants DMS-0505473the Natural Science Foundation of China under Grant NSFC-10728101,and the Royal Society-Wolfson Research Merit Award (UK)
文摘We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling fluid flows such as the blood flow through compliant axisyminetric vessels. Early models derived are nonconservative and/or nonho- mogeneous with measure source terms, which are endowed with infinitely many Riemann solutions for some Riemann data. In this paper, we derive a one-dimensional hyperbolic system that is conservative and homogeneous. Moreover, there exists a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data, under a natural stability entropy criterion. The Riemann solutions may consist of four waves for some cases. The system can also be written as a 3 × 3 system for which strict hyperbolicity fails and the standing waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue.
基金partially supported by the National Natural Science Foundation of China(11126189,11171259)Specialized Research Fund for the Doctoral Program of Higher Education(20120141120058)+1 种基金China Postdoctoral Science Foundation Funded Project(20110491212)the Fundamental Research Funds for the Central Universities(2042011111054)
文摘We obtain the Omori-Yau maximum principle on complete properly immersed submanifolds with the mean curvature satisfying certain condition in complete Riemannian manifolds whose radial sectional curvature satisfies some decay condition, which generalizes our previous results in [17]. Using this generalized maximum principle, we give an estimate on the mean curvature of properly immersed submanifolds in H^n × R^e with the image under the projection on H^n contained in a horoball and the corresponding situation in hyperbolic space. We also give other applications of the generalized maximum principle.
基金supported by the National Natural Science Foundation of China(No.11301566)the Postdoc Scholarship(No.2012M511900)
文摘In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the metric spaces under certain condi- tions. As an application, for a group G strongly relatively hyperbolic to a subgroup H, the author proves that B（n） = {g ∈ G／ │g│suЭe≤ n} admits a coarse embedding into a uniformly convex Banach space if H does.
文摘We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang’s previous result for modified asymptotically flat initial data sets.
基金Supported by the National Natural Science Foundation of China(Grant No.10926162)the Fundamental Research Funds for the Central Universities(Grant No.2009B01314)the Natural Science Foundation of HohaiUniversity(Grant No.2009428011)
文摘For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.
