Distributed matrix-scaled consensus is a kind of generalized cooperative control problem and has broad applications in the field of social network and engineering.This paper addresses the robust distributed matrix-sca...Distributed matrix-scaled consensus is a kind of generalized cooperative control problem and has broad applications in the field of social network and engineering.This paper addresses the robust distributed matrix-scaled consensus of perturbed multi-agent systems suffering from unknown disturbances.Distributed discontinuous protocols are first proposed to drive agents to achieve cluster consensus and suppress the effect of disturbances.Adaptive protocols with time-varying gains obeying differential equations are also designed,which are completely distributed and rely on no global information.Using the boundary layer technique,smooth protocols are proposed to avoid the unexpected chattering effect due to discontinuous functions.As a cost,under the designed smooth protocols,the defined matrix-scaled consensus error tends to a residual set rather than zero,in which the residual bound is arbitrary small by choosing proper parameters.Moreover,distributed dynamic event-based matrix-scalar consensus controllers are also proposed to avoid continuous communications.Simulation examples are provided to further verify the designed algorithms.展开更多
In this paper, we extend matrix scaled total least squares (MSTLS) problem with a single right-hand side to the case of multiple right-hand sides. Firstly, under some mild conditions, this paper gives an explicit expr...In this paper, we extend matrix scaled total least squares (MSTLS) problem with a single right-hand side to the case of multiple right-hand sides. Firstly, under some mild conditions, this paper gives an explicit expression of the minimum norm solution of MSTLS problem with multiple right-hand sides. Then, we present the Kronecker-product-based formulae for the normwise, mixed and componentwise condition numbers of the MSTLS problem. For easy estimation, we also exhibit Kronecker-product-free upper bounds for these condition numbers. All these results can reduce to those of the total least squares (TLS) problem which were given by Zheng et al. Finally, two numerical experiments are performed to illustrate our results.展开更多
基金supported in part by the National Key Research and Development Program of China(No.2020AAA0108905)by the National Natural Science Foundation of China(Nos.62103302,62273262,62088101)+7 种基金by the Shanghai Sailing Program(No.21YF1450300)by the Shanghai Chenguang Program(No.22CGA19)by the Shanghai Municipal Science and Technology Major Project(No.2021SHZDZX0100)by the Shanghai Science and Technology Planning Project(Nos.21ZR1466400,22QA1408500)by the Shanghai Municipal Commission of Science and Technology Project(No.19511132101)by the Fundamental Research Funds for the Central Universities(No.2022-5-YB-05)by the Industry,Education and Research Innovation Foundation of Chinese University(Nos.2021ZYA02008,2021ZYA03004)by the Special Fund for Independent Innovation of Aero Engine Corporation of China(No.ZZCX-2021-007).
文摘Distributed matrix-scaled consensus is a kind of generalized cooperative control problem and has broad applications in the field of social network and engineering.This paper addresses the robust distributed matrix-scaled consensus of perturbed multi-agent systems suffering from unknown disturbances.Distributed discontinuous protocols are first proposed to drive agents to achieve cluster consensus and suppress the effect of disturbances.Adaptive protocols with time-varying gains obeying differential equations are also designed,which are completely distributed and rely on no global information.Using the boundary layer technique,smooth protocols are proposed to avoid the unexpected chattering effect due to discontinuous functions.As a cost,under the designed smooth protocols,the defined matrix-scaled consensus error tends to a residual set rather than zero,in which the residual bound is arbitrary small by choosing proper parameters.Moreover,distributed dynamic event-based matrix-scalar consensus controllers are also proposed to avoid continuous communications.Simulation examples are provided to further verify the designed algorithms.
文摘In this paper, we extend matrix scaled total least squares (MSTLS) problem with a single right-hand side to the case of multiple right-hand sides. Firstly, under some mild conditions, this paper gives an explicit expression of the minimum norm solution of MSTLS problem with multiple right-hand sides. Then, we present the Kronecker-product-based formulae for the normwise, mixed and componentwise condition numbers of the MSTLS problem. For easy estimation, we also exhibit Kronecker-product-free upper bounds for these condition numbers. All these results can reduce to those of the total least squares (TLS) problem which were given by Zheng et al. Finally, two numerical experiments are performed to illustrate our results.
