5 papers
Reachability and asymptotics of Gaussian Transformer dynamics
Albert Alcalde, Zhengping Ji, Enrique Zuazua
We formulate data propagation through the Transformer, the machine learning architecture powering large language models, as a nonlinear control system on the space of probability m…
t-Product and t-STP of Cubic Matrices With Application to Hyper-Networked Systems
Daizhan Cheng, Zhengping Ji
Motivated by the study of dynamic control systems, this paper proposes novel algebraic operations on cubic matrices to construct both linear and nonlinear controlled dynamics. The…
Observer-Based Realization of Control Systems
Daizhan Cheng, Xiao Zhang, Zhengping Ji +1
A novel model reduction framework for large-scale complex systems is proposed by introducing function-type dynamic control systems via the dimension-keeping semi-tensor product (DK…
On Universal Eigenvalues and Eigenvectors of Hypermatrices
Daizhan Cheng, Zhengping Ji
A generalized eigenvector of a hypermatrix, called the universal (U-) eigenvector, is proposed, which extended the notion of diagonal (D-) eigenvectors in the literature. Using the…
On Control Networks Over Finite Lattices
Zhengping Ji, Daizhan Cheng
The modeling and control of networks over finite lattices are studied via the algebraic state space approach. Using the semi-tensor product of matrices, we obtain the algebraic sta…