scholarly journals Bipartite Consensus for Multiagent Systems via Event-Based Control

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Cui-Qin Ma ◽  
Wei-Guo Sun
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Balance Case ◽  
Control Gain ◽  
New Type ◽  
Bipartite Consensus ◽  
Necessary And Sufficient ◽  
Event Based ◽  
Selection Of

This paper studies bipartite consensus for first-order multiagent systems. To improve resource utilization, event-based protocols are considered for bipartite consensus. A new type of control gain is designed in the proposed protocols. By appropriate selection of control gains, the convergence rate of the closed-loop system can be adjusted. Firstly, for structural balance case, necessary and sufficient conditions are given on communication relations and consensus gains to achieve bipartite consensus. Secondly, for structural unbalance case, necessary and sufficient conditions are proposed to ensure the stabilizing of the system. It can be found that the system will not show Zeno behavior. Numerical simulations are used to demonstrate the theoretical results.

On the Preservation of Root Numbers and the Behavior of Weil Characters under Reciprocity Equivalence

1997 ◽  
Vol 40 (4) ◽  
pp. 402-415
Author(s):  
Jenna P. Carpenter
Keyword(s):  
Number Field ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Witt Ring ◽  
Root Numbers ◽  
Local Root ◽  
Necessary And Sufficient ◽  
Selection Of ◽  
Local Root Numbers

AbstractThis paper studies how the local root numbers and the Weil additive characters of the Witt ring of a number field behave under reciprocity equivalence. Given a reciprocity equivalence between two fields, at each place we define a local square class which vanishes if and only if the local root numbers are preserved. Thus this local square class serves as a local obstruction to the preservation of local root numbers. We establish a set of necessary and sufficient conditions for a selection of local square classes (one at each place) to represent a global square class. Then, given a reciprocity equivalence that has a finite wild set, we use these conditions to show that the local square classes combine to give a global square class which serves as a global obstruction to the preservation of all root numbers. Lastly, we use these results to study the behavior of Weil characters under reciprocity equivalence.

scholarly journals Geometric Approach to the Realization of Planar Elastic Behaviors With Mechanisms Having Four Elastic Components

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Sufficient Conditions ◽  
Geometric Approach ◽  
Necessary And Sufficient Conditions ◽  
Elastic Component ◽  
Elastic Behavior ◽  
Parallel Mechanisms ◽  
Compliant Joints ◽  
Necessary And Sufficient ◽  
Selection Of

This paper addresses the passive realization of any selected planar elastic behavior with redundant elastic manipulators. The class of manipulators considered are either serial mechanisms having four compliant joints or parallel mechanisms having four springs. Sets of necessary and sufficient conditions for mechanisms in this class to passively realize an elastic behavior are presented. The conditions are interpreted in terms of mechanism geometry. Similar conditions for nonredundant cases are highly restrictive. Redundancy yields a significantly larger space of realizable elastic behaviors. Construction-based synthesis procedures for planar elastic behaviors are also developed. In each, the selection of the mechanism geometry and the selection of joint/spring stiffnesses are completely decoupled. The procedures require that the geometry of each elastic component be selected from a restricted space of acceptable candidates.

scholarly journals Collective Coordination of High-Order Dynamic Multiagent Systems Guided by Multiple Leaders

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Xin-Lei Feng ◽  
Ting-Zhu Huang ◽  
Jin-Liang Shao
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Second Order ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Multiple Leaders ◽  
Theoretical Results

For second-order and high-order dynamic multiagent systems with multiple leaders, the coordination schemes that all the follower agents flock to the polytope region formed by multiple leaders are considered. Necessary and sufficient conditions which the follower agents can enter the polytope region by the leaders are obtained. Finally, numerical examples are given to illustrate our theoretical results.

scholarly journals The Cesáro Core of Double Sequences

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Kuddusi Kayaduman ◽  
Celal Çakan
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Double Sequences ◽  
Dimensional Matrix ◽  
New Type ◽  
Necessary And Sufficient

We have characterized a new type of core for double sequences, -core, and determined the necessary and sufficient conditions on a four-dimensional matrix to yield -core-core for all .

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