報告題目：From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems
報告概要：Motivated by the semi-tensor product of matrices, which is now called the M-product, a systematic dimension-free matrix theory is proposed. It consists of M-product, V-product of matrices; M-addition, V-addition of matrices/vectors; and M-equivalence, V-equivalence of matrices/vectors. All these operators with newly developed properties form the dimension-free matrix theory. Under this new framework, all the matrices with arbitrary dimensions form a vector space M, and all the vectors with arbitrary dimensions also form a vector space V. Certain further geometric structures are explored. For instance, the fiber bundle structure of M and V over equivalence classes is obtained.
Because both M and V are dimension-free, the action of M on V becomes a cross-dimensional linear system. The trajectory of the system is calculated and certain properties are revealed. The system is naturally developed to (discrete/continuous) cross-dimensional control systems. Finally, the cross-dimensional nonlinear (control) systems are also investigated.
Cross-dimensional system theory may be used to investigate dimension-varying systems such as internets, genetic networks; uncertain-dimensional systems such as superstring in theoretical physics; or engineering systems such as power generators.
Dr. Daizhan Cheng graduated from Tsinghua University in 1970, received M.S. from Graduate School, Chinese Academy of Sciences in 1981, and Ph.D. from Washington University, St. Louis, in 1985. Since 1990, he is a professor with Institute of Systems Science, AMSS, Chinese Academy of Sciences. He is the author/coauthor of 14 Books, over 270 Journal Papers and over 160 Conference Papers. He was member of IEEE CSS Board of Governors (2009, 2015), and IFAC Council Member (2011-2014). He is IEEE Fellow (2006-),IFAC Fellow (2008-). He received Second National Natural Science Award twice (in 2008 and 2014), Outstanding Science and Technology Achievement Price of CAS (2015), and the Automatica Best Paper Award (2008-2010), bestowed by IFAC.