3 citations · 8 across the 16 of their papers we have counts for
16 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 an application to hyper-networked systems
Daizhan Cheng, Zhengping Ji
Control systems with tensor-valued state transitions require a product that specifies both how coefficients act on each frontal slice and how different slices interact. This paper…
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…
Contracted Product of Hypermatrices via STP of Matrices
Daizhan Cheng, Min Meng, Xiao Zhang +1
An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion of different matrix expressi…
Transition System Representation of Boolean Control Networks
Daizhan Cheng, Xiao Zhang, Zhengping Ji
First, the topological structure of a transition system is studied. Then, two types of transition system (TS) representations of Boolean networks (BNs) and Boolean control networks…
Aggregated (Bi-)Simulation of Finite Valued Networks
Zhengping Ji, Xiao Zhang, Daizhan Cheng
The paper provides a method to approximate a large-scale finite-valued network by a smaller model called the aggregated simulation, which is a combination of aggregation and (bi-)s…
Semi-Tensor Product of Hypermatrices with Application to Compound Hypermatrices
Daizhan Cheng, Xiao Zhang, Zhengping Ji
The semi-tensor product (STP) of matrices is extended to the STP of hypermatrices. Some basic properties of the STP of matrices are extended to the STP of hypermatrices. The hyperd…
Analysis of Discrete-Time Switched Linear Systems under Logic Dynamic Switchings
Xiao Zhang, Min Meng, Zhengping Ji
The control properties of discrete-time switched linear systems (SLS) with switching signals generated by logical dynamic systems are studied using the semi-tensor product (STP) ap…
Invariant and Dual Invariant Subspaces of -valued Networks
Daizhan Cheng, Hongsheng Qi, Xiao Zhang +1
Consider a -valued network. Two kinds of (control) invariant subspaces, called state and dual invariant subspaces, are proposed, which are subspaces of state space and dual spac…
Global Controllability Criteria and Motion Planning of Regular Affine Systems With Drifts
Zhengping Ji, Xiao Zhang, Daizhan Cheng
In this article, we give a condition for the global controllability of affine nonlinear control systems with drifts on Euclidean spaces. Under regularity assumptions, the condition…
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…
From Dimension-Free Manifolds to Dimension-varying Control Systems
Daizhan Cheng, Zhengping Ji
Starting from the vector multipliers, the inner product, norm, distance, as well as addition of two vectors of different dimensions are proposed, which makes the spaces into a topo…
Hidden Order of Boolean Networks
Xiao Zhang, Zhengping Ji, Daizhan Cheng
It is a common belief that the order of a Boolean network is mainly determined by its attractors, including fixed points and cycles. Using semi-tensor product (STP) of matrices and…
Weighted and Near Weighted Potential Games with Application to Game Theoretic Control
Daizhan Cheng, Zhengping Ji
An algorithm is proposed to verify whether a finite game is a weighted potential game (WPG) without pre-knowledge on its weights. Then the algorithm is also applied to find the clo…
On Perfect Hypercomplex Algebra
Daizhan Cheng, Zhengping Ji
The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebra (PHA) is investigated. Necessary and sufficient conditions for an algebra to be…