Kuize Zhang
Harbin Engineering University
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Publication
Featured researches published by Kuize Zhang.
IEEE Transactions on Neural Networks | 2013
Lijun Zhang; Kuize Zhang
This brief investigates the controllability and observability of Boolean control networks with (not necessarily bounded) time-variant delays in states. After a brief introduction to converting a Boolean control network to an equivalent discrete-time bilinear dynamical system via the semi-tensor product of matrices, the system is split into a finite number of subsystems (constructed forest) with no time delays by using the idea of splitting time that is proposed in this brief. Then, the controllability and observability of the system are investigated by verifying any so-called controllability constructed path and any so-called observability constructed paths in the above forest, respectively, which generalize some recent relevant results. Matrix test criteria for the controllability and observability are given. The corresponding control design algorithms based on the controllability theorems are given. We also show that the computing complexity of our algorithm is much less than that of the existing algorithms.
Automatica | 2015
Kuize Zhang; Lijun Zhang; Lihua Xie
Invertibility is an interesting and classical control-theoretic problem. However, there has been no result for the invertibility of Boolean control networks (BCNs) so far. We first adopt the theory of symbolic dynamics to characterize it. First, it is shown that a BCN generates a continuous mapping from the space of input trajectories to the space of output trajectories. Based on it, the concepts of nonsingularity and invertibility of BCNs are first defined as the injectivity and bijectivity of the mapping, respectively. Second, combined symbolic dynamics with the semi-tensor product (STP) of matrices, an equivalent test criterion for invertibility is given; easily computable algorithms to construct the inverse BCN for an invertible BCN are presented; and it is proved that invertibility remains invariant under coordinate transformations. Third, an equivalent test criterion for nonsingularity is given via defining a novel directed graph that is called weighted pair graph. Lastly, as an application of invertibility to systems biology, we prove that the BCN model proposed in Faure et?al. (2006) is not invertible, i.e., we prove that arbitrarily controlling mammalian cell cycles is unfeasible at the theoretical level.
Applied Mathematics and Computation | 2009
Changjiang Bu; Min Li; Kuize Zhang; Lan Zheng
Let M=ABCD (A is square) be a square block matrix with an invertible subblock over a skew field K. In this paper, we give the necessary and sufficient conditions for the existence as well as the expressions of the group inverse for M under some conditions.
IEEE Transactions on Automatic Control | 2016
Kuize Zhang; Lijun Zhang
The problem on how to determine the observability of Boolean control networks (BCNs) has been open for five years already. In this technical note, we propose a unified approach to determine all the four types of observability of BCNs in the literature. We define the concept of weighted pair graphs for BCNs. In the sense of each observability, we use the so-called weighted pair graph to transform a BCN to a finite automaton, and then we use the automaton to determine observability. In particular, the two types of observability that rely on initial states and inputs in the literature are determined. Finally, we show that no pairs of the four types of observability are equivalent, which reveals the essence of nonlinearity of BCNs.
Science in China Series F: Information Sciences | 2013
Lijun Zhang; Kuize Zhang
This paper investigates the controllability of time-variant Boolean control networks (BCNs). For the time-variant BCNs, a necessary and sufficient condition for the controllability is given, and a control design algorithm is presented. For a BCN with finite memories, an equivalent transformation to a time-variant BCN is constructed. Then a necessary and sufficient condition for the controllability and a control design algorithm are obtained.
Linear & Multilinear Algebra | 2011
Changjiang Bu; Kuize Zhang; Jiemei Zhao
In 1983, Campbell proposed a problem to find an explicit representation of the Drazin inverse for the block matrix with E and F square in terms of E and F according to the research on singular differential equations. In this article, we give the representations of the Drazin inverse for with E and F square under the condition that EF = FE and the Drazin inverse for with E square under the condition that EFG = FGE, and then give some representations under some other conditions, so as to solve the problem partially and to get some extra results.
Linear & Multilinear Algebra | 2010
Changjiang Bu; Kuize Zhang; Jiemei Zhao
Let K be any skew field and K m×n be the set of all the m × n matrices over K. In this article, necessary and sufficient conditions are given for the existence of the group inverses of block matrix , where and exist, A = c 1 B + c 2 C, non-zero elements c 1 and c 2 are in the centre of K and block matrix , where A = B k C l , k and l are positive integers. Then the representations of the group inverses of these block matrices are also given.
IEEE Transactions on Automatic Control | 2016
Daizhan Cheng; Ting Liu; Kuize Zhang; Hongsheng Qi
This note provides the detailed description of the decomposed subspaces of finite games. First, the basis of potential games and the basis of non-strategic games are revealed. Then the bases of pure potential and pure harmonic subspaces are also obtained. These bases provide an explicit formula for the decomposition, and are convenient for investigating the properties of the corresponding subspaces. As an application, we consider the dynamics of networked evolutionary games (NEGs). Three problems are considered: 1) the dynamic equivalence of evolutionary games; 2) the dynamics of near potential games; and 3) the decomposition of NEGs.
Applied Mathematics and Computation | 2012
Kuize Zhang; Changjiang Bu
In this paper, new equivalent conditions for the existence of group inverses of matrices over a right Ore domain (or a Bezout domain) are given. Utilizing these equivalent conditions, equivalent conditions for the existence and representations of the group inverses of block matrix AB0C over a right Ore domain and block matrix AAC0 over a Bezout domain are given, where A and C are square, which generalize some recent relative results.
Electronic Journal of Linear Algebra | 2009
Changjiang Bu; Jiemei Zhao; Kuize Zhang
In this paper, necessary and sufficient conditions are given for the existence of the group inverse of the block matrix A A B 0 over any skew field, where A, B are both square and rank(B) ≥ rank(A). The representation of this group inverse and some relative additive results are also given.