This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol i...This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol is proposed, and consensus convergence of multigent systems is analyzed based on the Lyapunov stability theory. The consensus problem can be formulated into solving a feasible problem with bilinear matrix inequality （BMI） constrains. Furthermore, the consensus protocol is extended to achieving tracking and formation control. By introducing the formation structure set, each agent can gain its individual desired trajectory. Finally, numerical simulations are provided to show the effectiveness of our strategies. The results show that agents from arbitrary initial states can asymptotically reach a consensus. In addition, agents with high-dimensional can track any target trajectory, and maintain desired formation during movement by selecting appropriate structure set.展开更多
Determining the number of chemical species is the first step in analyses of a chemical or biological system. A novel method is proposed to address this issue by taking advantage of frequency differences between chemic...Determining the number of chemical species is the first step in analyses of a chemical or biological system. A novel method is proposed to address this issue by taking advantage of frequency differences between chemical information and noise. Two interlaced submatrices were obtained by downsampling an original data spectra matrix in an interlacing manner. The two interlaced submatrices contained similar chemical information but different noise levels. The number of relevant chemical species was determined through pairwise comparisons of principal components obtained by principal component analysis of the two interlaced submatrices. The proposed method, referred to as SRISM, uses two self-referencing interlaced submatrices to make the determination. SRISM was able to selectively distinguish relevant chemical species from various types of interference factors such as signal overlapping, minor components and noise in simulated datasets. Its performance was further validated using experimental datasets that contained high-levels of instrument aberrations, signal overlapping and collinearity. SRISM was also applied to infrared spectral data obtained from atmospheric monitoring. It has great potential for overcoming various types of interference factor. This method is mathematically rigorous, computationally efficient, and readily automated.展开更多
A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational iden...A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.展开更多
基金Supported by the National Natural Science Foundation of China （No. 61075065,60774045, U1134108） and the Ph. D Programs Foundation of Ministry of Education of China （ No. 20110162110041 ）.
文摘This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol is proposed, and consensus convergence of multigent systems is analyzed based on the Lyapunov stability theory. The consensus problem can be formulated into solving a feasible problem with bilinear matrix inequality （BMI） constrains. Furthermore, the consensus protocol is extended to achieving tracking and formation control. By introducing the formation structure set, each agent can gain its individual desired trajectory. Finally, numerical simulations are provided to show the effectiveness of our strategies. The results show that agents from arbitrary initial states can asymptotically reach a consensus. In addition, agents with high-dimensional can track any target trajectory, and maintain desired formation during movement by selecting appropriate structure set.
基金supported by the Program for Changjiang Scholars and Innovative Research Team in University and Fundamental Research Funds for the Central Universities(wk2060190040)
文摘Determining the number of chemical species is the first step in analyses of a chemical or biological system. A novel method is proposed to address this issue by taking advantage of frequency differences between chemical information and noise. Two interlaced submatrices were obtained by downsampling an original data spectra matrix in an interlacing manner. The two interlaced submatrices contained similar chemical information but different noise levels. The number of relevant chemical species was determined through pairwise comparisons of principal components obtained by principal component analysis of the two interlaced submatrices. The proposed method, referred to as SRISM, uses two self-referencing interlaced submatrices to make the determination. SRISM was able to selectively distinguish relevant chemical species from various types of interference factors such as signal overlapping, minor components and noise in simulated datasets. Its performance was further validated using experimental datasets that contained high-levels of instrument aberrations, signal overlapping and collinearity. SRISM was also applied to infrared spectral data obtained from atmospheric monitoring. It has great potential for overcoming various types of interference factor. This method is mathematically rigorous, computationally efficient, and readily automated.
基金Project supported by the State Administration of Foreign Experts Affairs of Chinathe National Natural Science Foundation of China (Nos.10971136,10831003,61072147,11071159)+3 种基金the Chunhui Plan of the Ministry of Education of Chinathe Innovation Project of Zhejiang Province (No.T200905)the Natural Science Foundation of Shanghai (No.09ZR1410800)the Shanghai Leading Academic Discipline Project (No.J50101)
文摘A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.
