scholarly journals Consensus Analysis of Fractional-Order Multiagent Systems with Double-Integrator

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Chunde Yang ◽  
Wenjing Li ◽  
Wei Zhu
Keyword(s):  
Multiagent Systems ◽  
Fractional Order ◽  
Spanning Tree ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Consensus Analysis ◽  
Directed Spanning Tree ◽  
Necessary And Sufficient ◽  
Theoretical Results ◽  
Double Integrator

In nature, many phenomena can be explained by coordinated behavior of agents with fractional-order dynamics. In this paper, the consensus problem of fractional-order multiagent systems with double-integrator is studied, where the fractional-order satisfies0<α<2. Based on the fractional-order stability theory, Mittag-Leffler function, and Laplace transform, a necessary and sufficient condition is obtained under the assumption that the directed graph for the communication network contains a directed spanning tree. Finally, an example with simulation is presented to illustrate the theoretical results.

scholarly journals Consensus of Heterogeneous Multiagent Systems with Switching Dynamics

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Wenshuai Wang ◽  
Juling Wang ◽  
Huaizhu Wang ◽  
Yuanshi Zheng
Keyword(s):  
Multiagent Systems ◽  
Spanning Tree ◽  
Matrix Theory ◽  
Nonnegative Matrix ◽  
Time Dynamics ◽  
Switching Dynamics ◽  
Directed Spanning Tree ◽  
Interaction Topology ◽  
Theoretical Results ◽  
Double Integrator

Heterogeneity is an important feature of multiagent systems. This paper addresses the consensus problem of heterogeneous multiagent systems composed of first-integrator and double-integrator agents. The dynamics of each agent switches between continuous-time and discrete-time dynamics. By using the graph theory and nonnegative matrix theory, we derive that the system can achieve consensus if and only if the fixed interaction topology has a directed spanning tree. For switching topologies, we get that the system can reach consensus if each interaction topology has a directed spanning tree. Simulation examples are provided to demonstrate the effectiveness of our theoretical results.

Finding Cut-Edges and the Minimum Spanning Tree via Semi-Tensor Product Approach

2018 ◽  
Vol 6 (5) ◽  
pp. 459-472
Author(s):  
Xujiao Fan ◽  
Yong Xu ◽  
Xue Su ◽  
Jinhuan Wang
Keyword(s):  
Tensor Product ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Matrix ◽  
Product Approach ◽  
Matrix Expression ◽  
Necessary And Sufficient ◽  
Logical Functions

Abstract Using the semi-tensor product of matrices, this paper investigates cycles of graphs with application to cut-edges and the minimum spanning tree, and presents a number of new results and algorithms. Firstly, by defining a characteristic logical vector and using the matrix expression of logical functions, an algebraic description is obtained for cycles of graph, based on which a new necessary and sufficient condition is established to find all cycles for any graph. Secondly, using the necessary and sufficient condition of cycles, two algorithms are established to find all cut-edges and the minimum spanning tree, respectively. Finally, the study of an illustrative example shows that the results/algorithms presented in this paper are effective.

scholarly journals Consensus of Third-Order Multiagent Systems with Time Delay in Undirected Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Yanfen Cao ◽  
Yuangong Sun
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Continuous Time ◽  
Matrix Analysis ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Third Order ◽  
Necessary And Sufficient ◽  
Frequency Domain Approach ◽  
Order Continuous

We consider consensus of a class of third-order continuous-time multiagent systems with time delay in undirected networks. By using matrix analysis and a frequency domain approach, a necessary and sufficient condition for consensus is established. A simulation result is also given to illustrate the main theoretical result.

Representation of holomorphic functions by schlömilch’s series

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Peter Rusev
Keyword(s):  
Bessel Function ◽  
Fractional Order ◽  
Holomorphic Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Zero Index

AbstractA necessary and sufficient condition is given for holomorphic functions to be represented by series of the kind $\sum\limits_{n = 0}^\infty {a_n J_0 (nz),z,a_n \in \mathbb{C},} $ where J 0(z) is the Bessel function of first kind with zero index. To derive the result, we use an Erdélyi-Kober operator of fractional order.

scholarly journals Consensus Analysis for Third-Order Multiagent Systems in Directed Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yanfen Cao ◽  
Yuangong Sun
Keyword(s):  
Dynamical Systems ◽  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Laplacian Matrix ◽  
Consensus Problem ◽  
Third Order ◽  
Consensus Analysis ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Theoretical Results

We investigate consensus problem for third-order multiagent dynamical systems in directed graph. Necessary and sufficient conditions to consensus of third-order multiagent systems have been established under three different protocols. Compared with existing results, we focus on the relationship between the scaling strengths and the eigenvalues of the involved Laplacian matrix, which guarantees consensus of third-order multiagent systems. Finally, some simulation examples are given to illustrate the theoretical results.

scholarly journals Study of “Sticking and Restarting Phenomenon” in Electropneumatic Positioning Systems

2005 ◽  
Vol 127 (1) ◽  
pp. 173-184 ◽  
Author(s):  
Xavier Brun ◽  
Sylvie Sesmat ◽  
Daniel Thomasset ◽  
Serge Scavarda
Keyword(s):  
Dry Friction ◽  
Partial Equilibrium ◽  
Experimental Result ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Pressure Force ◽  
Friction Forces ◽  
Positioning Systems ◽  
Necessary And Sufficient ◽  
Theoretical Results

This paper explains the possible occurrence of the “sticking and restarting phenomenon” observed with electropneumatic positioning systems. This is carried out from the notion of partial equilibrium, with the analysis of the model which incorporates two parallel phenomena which are used to generate a pressure force subjected to dry friction forces. Also, an experimental result has been studied in a particular pressure force plane which shows the origin of the problem more explicitly. The theoretical results give a necessary and sufficient condition for the restarting phenomenon not to occur and, if this condition is not validated, there is an estimation of the restarting time. Understanding this undesirable phenomenon will be the basis for further work which will attempt to find solutions to avoid its occurrence.

scholarly journals Consensus of Discrete Time Second-Order Multiagent Systems with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Zhu
Keyword(s):  
Time Delay ◽  
Convergence Rate ◽  
Theoretical Result ◽  
Multiagent Systems ◽  
Discrete Time ◽  
Second Order ◽  
Sufficient Condition ◽  
Consensus Problem ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The consensus problem for discrete time second-order multiagent systems with time delay is studied. Some effective methods are presented to deal with consensus problems in discrete time multiagent systems. A necessary and sufficient condition is established to ensure consensus. The convergence rate for reaching consensus is also estimated. It is shown that arbitrary bounded time delay can safely be tolerated. An example is presented to illustrate the theoretical result.

scholarly journals Synchronization of a Generalized High-dimensional Kuramoto Model With Directed Graphs

2021 ◽  
Author(s):  
Jinxing Zhang ◽  
Jiandong Zhu ◽  
Xiaodi Li
Keyword(s):  
Directed Graph ◽  
Directed Graphs ◽  
Kuramoto Model ◽  
High Dimensional ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Initial State ◽  
Necessary And Sufficient ◽  
Theoretical Results

Abstract In this paper, a generalized high-dimensional Kuramoto model with directed graphs is investigated. A necessary and sufficient condition for equilibria is given and the synchronization is proved under weaker directed graph conditions and more general initial state constrains. Finally, an example is given to validate the theoretical results.

scholarly journals Fractional-order LCL filters: principle, frequency characteristics, and their analysis

2021 ◽  
Author(s):  
Junhua Xu ◽  
Xiaocong Li ◽  
Xueli Luo ◽  
Liliang Hou ◽  
Jianbo Qin ◽  
...  
Keyword(s):  
Fractional Order ◽  
Theoretical Basis ◽  
Digital Simulation ◽  
Frequency Characteristics ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Operating Characteristics ◽  
Theoretical Derivation ◽  
Integer Order ◽  
Necessary And Sufficient

Abstract In this paper, a fractional-order LCL (FOLCL) filter is constructed by introducing fractional-order inductors (FOIs) and fractional-order capacitors (FOCs) to replace the inductors and capacitors in a traditional integer-order LCL (IOLCL) filter, respectively. The principle and frequency characteristics of an FOLCL filter are systematically studied, and five important properties are derived and demonstrated in-depth. One of the most important achievements is that we discover the necessary and sufficient condition for the existence of resonance for an FOLCL filter, that is, the sum of the order of the FOIs and the FOC is equal to 2, which provides a theoretical basis for avoiding the resonance of an FOLCL filter effectively in design. The correctness of the theoretical derivation and analysis are verified by digital simulation. Compared with an IOLCL filter, an FOLCL filter presents more flexible and diverse operating characteristics and has a broader application prospect.

scholarly journals Consensus of Fractional-Order Multiagent Systems with Double Integrator under Switching Topologies

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Shiyun Shen ◽  
Wenjing Li ◽  
Wei Zhu
Keyword(s):  
Numerical Simulation ◽  
Laplace Transform ◽  
Theoretical Result ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Dwell Time ◽  
Sufficient Condition ◽  
Switching Topologies ◽  
Double Integrator

Due to the complexity of the practical environments, many systems can only be described with the fractional-order dynamics. In this paper, the consensus of fractional-order multiagent systems with double integrator under switching topologies is investigated. By applying Mittag-Leffler function, Laplace transform, and dwell time technique, a sufficient condition on consensus is obtained. Finally, a numerical simulation is presented to illustrate the effectiveness of the theoretical result.

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