Mix-valued logic-based formation control

Zhang, Lequn; Feng, Jun‐e

doi:10.1080/00207179.2013.787550

Cited by 19 publications

(9 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main difference is that in logicbased multi-agent systems, agents are allowed to perform logical operations, while in finite-field networks, agents only perform modular addition and multiplication. Thus, the results obtained in [28,38] cannot be applied to the consensus analysis of finite-field networks.…”

Section: Introductionmentioning

confidence: 90%

“…In [28], Lou and Hong presented some necessary and sufficient conditions for the social decision in a switching Boolean network where each agent has its private information. Zhang and Feng [38] studied the formation control problem of a mix-valued logic-based multiagent system, and proposed a new design method for this problem via STP. It should be pointed out that finite-field networks studied in this paper are different from logic-based multi-agent systems.…”

Section: Introductionmentioning

confidence: 99%

“…It is noted that STP has also been applied to the consensus analysis [28] and formulation control [38] of logic-based multi-agent systems. In [28], Lou and Hong presented some necessary and sufficient conditions for the social decision in a switching Boolean network where each agent has its private information.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Consensus of finite-field networks with switching topologies and linear protocols

Wang

Guo

2014

Proceedings of the 33rd Chinese Control Conference

View full text Add to dashboard Cite

This paper investigates the consensus of finite-field networks with switching topologies and linear protocols by using the semi-tensor product (STP) method, and presents a number of new results. First, an algebraic form of finite-field networks with switching topologies and linear protocols is obtained via STP. Second, based on the algebraic form and the switching point reachability, a necessary and sufficient condition is presented for the consensus of finite-field networks under arbitrary switching signal. Finally, an illustrative example is given to verify the obtained new results. The study of the illustrative example shows that the new results presented in this paper are very effective in the consensus analysis of finite-field networks with switching topologies and linear protocols under arbitrary switching signal.

show abstract

Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Consensus of finite-field networks with switching topologies and linear protocols

Wang

Guo

2014

Proceedings of the 33rd Chinese Control Conference

View full text Add to dashboard Cite

show abstract

“…This is witnessed by hundreds of research papers. A multitude of applications of STP include (i) logical dynamic systems [6], [18], [32]; (ii) systems biology [54], [20]; (iii) graph theory and formation control [45], [55]; (iv) circuit design and failure detection [33], [34], [9]; (v) game theory [21], [10], [11]; (vi) finite automata and symbolic dynamics [50], [57], [23]; (vii) coding and cryptography [58], [56]; (viii) fuzzy control [8], [17]; (ix) some engineering applications [49], [36]; and many other topics [7], [38], [52], [59], [60], [37]; just to name a few.…”

Section: Introductionmentioning

confidence: 99%

On equivalence of matrices

Cheng

2019

Asian Journal of Mathematics

View full text Add to dashboard Cite

A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related structures and properties are investigated. Then the generalized matrix addition is also introduced, which extends the classical matrix addition to a class of two matrices with different dimensions.Motivated by STP of matrices, two kinds of equivalences of matrices (including vectors) are introduced, which are called matrix equivalence (M-equivalence) and vector equivalence (V-equivalence) respectively. The lattice structure has been established for each equivalence. Under each equivalence, the corresponding quotient space becomes a vector space. Under Mequivalence, many algebraic, geometric, and analytic structures have been posed to the quotient space, which include (i) lattice structure; (ii) inner product and norm (distance); (iii) topology; (iv) a fiber bundle structure, called the discrete bundle; (v) bundled differential manifold; (vi) bundled Lie group and Lie algebra. Under V-equivalence, vectors of different dimensions form a vector space V, and a matrix A of arbitrary dimension is considered as an operator (linear mapping) on V. When A is a bounded operator (not necessarily square but includes square matrices as a special case), the generalized characteristic function, eigenvalue and eigenvector etc. are defined.In one word, this new matrix theory overcomes the dimensional barrier in certain sense. It provides much more freedom for using matrix approach to practical problems.

show abstract

“…Then, one can analyze Boolean (control) networks by using the classical control theory. Up to now, there have been many interesting works on the control of BCNs via this novel method, which include controllability and observability (Chen & Sun, 2014;Cheng, Li, & Qi, 2010;Cheng & Qi, 2009Feng, Yao, & Cui, 2012;Fornasini & Valcher, 2013a;Laschov & Margaliot, 2012;Li & Sun, 2011a,b;Li & Wang, 2012;Zhao, Cheng, & Qi, 2010), disturbance decoupling (Cheng, 2011;, optimal control (Fornasini & Valcher, 2014;Laschov & Margaliot, 2011;Zhao, Li, & Cheng, 2011), stability and stabilization (Cheng, Qi, Li, & Liu, 2011;Li & Wang, 2013;, and other control problems (Cheng & Xu, 2013;Fornasini & Valcher, 2013b;Li & Chu, 2012;Wang, Zhang, & Liu, 2012;Xu & Hong, 2013;Zhang, 2012;Zhang & Feng, 2013;Zhao, Kim, & Filippone, 2013;Zou & Zhu, 2014).…”

mentioning

confidence: 99%