In this paper, the target aggregation is investigated for a multi-agent system consisting of second-order agents and multiple leaders. Sufficient conditions are proposed to make the agents approach the target set span...In this paper, the target aggregation is investigated for a multi-agent system consisting of second-order agents and multiple leaders. Sufficient conditions are proposed to make the agents approach the target set spanned by these moving leaders. With the condition on switching interconnection topologies, all mobile agents can asymptotically track the dynamical target set specified by multiple moving leaders with bounded error. Moreover, discussion on the case with static leaders is also given.展开更多
This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a ...This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. The main difficulty, when passing to the limit, is that the solution of the problems converges neither strongly in L^2(Ω) nor almost everywhere in Ω. A new convergence result involving nonlinear functions provides suitable weak convergence results which permit passing to the limit without using any extension operator.Consequently, using a corrector result proved in [Chourabi, I. and Donato, P., Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptotic Analysis, 92(1), 2015, 1–43, DOI: 10.3233/ASY-151288], the authors describe the limit problem, presenting a limit nonlinearity which is different for the two cases, that of a Neumann datum with a nonzero average and with a zero average.展开更多
基金supported in part by the National Natural Science Foundation of China under Grant Nos. 60874018,60736022,and 60821091
文摘In this paper, the target aggregation is investigated for a multi-agent system consisting of second-order agents and multiple leaders. Sufficient conditions are proposed to make the agents approach the target set spanned by these moving leaders. With the condition on switching interconnection topologies, all mobile agents can asymptotically track the dynamical target set specified by multiple moving leaders with bounded error. Moreover, discussion on the case with static leaders is also given.
文摘This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. The main difficulty, when passing to the limit, is that the solution of the problems converges neither strongly in L^2(Ω) nor almost everywhere in Ω. A new convergence result involving nonlinear functions provides suitable weak convergence results which permit passing to the limit without using any extension operator.Consequently, using a corrector result proved in [Chourabi, I. and Donato, P., Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptotic Analysis, 92(1), 2015, 1–43, DOI: 10.3233/ASY-151288], the authors describe the limit problem, presenting a limit nonlinearity which is different for the two cases, that of a Neumann datum with a nonzero average and with a zero average.
