scholarly journals Consensus of Fractional-Order Multiagent Systems with Nonuniform Time Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Jun Liu ◽  
Kaiyu Qin ◽  
Wei Chen ◽  
Ping Li ◽  
Mengji Shi
Keyword(s):  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
External Environment ◽  
Domain Theory ◽  
Dynamical Model ◽  
Integer Order ◽  
The Laplace Transform ◽  
Simulation Results ◽  
Theoretical Results

Due to the complex external environment, many multiagent systems cannot be precisely described or even cannot be described by an integer-order dynamical model and can only be described by a fractional-order dynamical model. In this paper, consensus problems are investigated for two types of fractional-order multiagent systems (FOMASs) with nonuniform time delays: FOMAS with symmetric time delays and undirected topology and FOMAS with asymmetric time delays and directed topology. Employing the Laplace transform and the frequency-domain theory, two delay margins are obtained to guarantee the consensus for the two types of FOMAS, respectively. These results are also suitable for the integer-order dynamical model. Finally, simulation results are provided to illustrate the effectiveness of our theoretical results.

scholarly journals Consensus of Delayed Fractional-Order Multiagent Systems Based on State-Derivative Feedback

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Liu ◽  
Kaiyu Qin ◽  
Wei Chen ◽  
Ping Li
Keyword(s):  
Graph Theory ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Multiagent System ◽  
Frequency Domain Analysis ◽  
Consensus Control ◽  
Control Protocol ◽  
Analysis Theory ◽  
Theoretical Results

A state-derivative feedback (SDF) is added into the designed control protocol in the existing paper to enhance the robustness of a fractional-order multiagent system (FMS) against nonuniform time delays in this paper. By applying the graph theory and the frequency-domain analysis theory, consensus conditions are derived to make the delayed FMS based on state-derivative feedback reach consensus. Compared with the consensus control protocol designed in the existing paper, the proposed SDF control protocol with nonuniform time delays can make the FMS with SDF and nonuniform time delays tolerate longer time delays, which means that the convergence speed of states of the delayed FMS with SDF is accelerated indirectly. Finally, the corresponding results of simulation are given to verify the feasibility of our theoretical results.

scholarly journals Consensus Conditions for a Class of Fractional-Order Nonlinear Multiagent Systems with Constant and Time-Varying Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiaorong Zhang ◽  
Min Shi
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Constant Time Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay ◽  
Theoretical Results

The consensus problem for a class of fractional-order nonlinear multiagent systems with a distributed protocol containing input time delay is investigated in this paper. Consider both cases of constant time delay and time-varying delay, the delay-independent consensus conditions are obtained to achieve the consensus of the systems, respectively, by adopting the linear matrix inequality (LMI) methods and stability theory of fractional-order systems. As illustrated by the numerical examples, the proposed theoretical results work well and accurately.

OPCL Coupling of Mixed Integer-Fractional Order oscillators: Tree and Chain Implementation

2021 ◽  
Author(s):  
Adedayo Oke Adelakun
Keyword(s):  
Fractional Order ◽  
Mixed Integer ◽  
Complete Synchronization ◽  
Amplitude Death ◽  
Integer Order ◽  
Simulation Results ◽  
Coupled Circuits ◽  
Tree Type ◽  
Chain Type

Abstract OPCL Coupling of Integer-order and fractional-order Sprott-A systems using off-shelf components are constructed. Fractance configurations such as chain-type and tree-type were designed using a fractional-order capacitor and fractional-order resistor, respectively. The simulation results of the coupled circuits reveal the transition between complete synchronization (CS) to Anti-synchronization (AS) and vice versa via Amplitude death (AD).

scholarly journals Consensus of Multiagent Systems with Directed Topology and Communication Time Delay Bases on the Laplace Transform

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Bo Liu ◽  
Li Wang ◽  
Dehui Sun ◽  
Xinmao Zhu
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Multiagent Systems ◽  
Consensus Problem ◽  
Directed Topology ◽  
Communication Time ◽  
The Laplace Transform ◽  
Initial States ◽  
Directed Topologies ◽  
Theoretical Results

This paper investigates the consensus problem of multiagent systems with directed topologies. Different from the literatures, a new method, the Laplace transform, to study the consensus of multiagent systems with directed topology and communication time delay is proposed. The accurate state of the consensus center and the upper bound of the communication delay to make the agents reach consensus are given. It is proved that all the agents could aggregate and eventually form a cohesive cluster in finite time under certain conditions, and the consensus center is only determined by the initial states and the communication configuration among the agents. Finally, simulations are given to illustrate the theoretical results.

Distributed coordination of fractional order multi-agent systems with communication delays

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Hong-yong Yang ◽  
Xun-lin Zhu ◽  
Ke-cai Cao
Keyword(s):  
Fractional Order ◽  
Communication Delays ◽  
Distributed Coordination ◽  
Multi Agent Systems ◽  
Order Model ◽  
Agent Systems ◽  
Integer Order ◽  
Dynamical Characteristics ◽  
The Laplace Transform ◽  
Multi Agent

AbstractBecause of the complexity of the practical environments, many distributed multi-agent systems can not be illustrated with the integer-order dynamics and can only be described with the fractional-order dynamics. Under the connected network with directed weighted topologies, the dynamical characteristics of agents with fractional-order derivative operator is analyzed in this paper. Applying the Laplace transform and frequency domain theory of the fractional-order operator, the distributed coordination of fractional-order multi-agent systems (FOMAS) with communication delays is studied, and a critical value of time delay is obtained to ensure the consensus of FOMAS. Since the integer-order model is a special case of fractional-order model, the extended results in this paper are in accordance with that of the integer-order model. Finally, numerical examples are provided to verify our results.

scholarly journals Couple-Group Consensus: A Class of Delayed Heterogeneous Multiagent Systems in Competitive Networks

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Lianghao Ji ◽  
Yue Zhang ◽  
Yiliu Jiang
Keyword(s):  
Multiagent Systems ◽  
Time Delays ◽  
Heterogeneous Systems ◽  
Velocity Estimation ◽  
Communication Delays ◽  
Group Consensus ◽  
Distributed Coordination ◽  
First Order ◽  
Communication Time ◽  
Theoretical Results

This paper discusses the couple-group consensus issues of a class of heterogeneous multiagent systems containing first-order and second-order dynamic agents under the influence of both input and communication delays. In distinction to the existing works, a novel distributed coordination control protocol is proposed which is not only on the foundation of the competitive interaction between the agents but also has no virtual velocity estimation in the first-order dynamics. Furthermore, without the restrictive assumptions existing commonly in the related works, several sufficient algebraic criteria are established for the heterogeneous systems to realize couple-group consensus asymptotically. The obtained conclusions show that the achievement of the systems’ couple-group consensus intimately relates to the coupling weights between the agents, the systems control parameters, and the input time delays of the agents, while communication time delays between the agents are irrelevant to it. Finally, several simulations are illustrated to verify the effectiveness of the obtained theoretical results.

scholarly journals Consensus of Multiagent Systems with Sampled Information and Noisy Measurements

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zhao-Jun Tang ◽  
Ting-Zhu Huang ◽  
Jin-Liang Shao
Keyword(s):  
Multiagent Systems ◽  
Directed Network ◽  
First Order ◽  
Network Topologies ◽  
Strong Consensus ◽  
Measurement Noises ◽  
Simulation Results ◽  
Approximation Type ◽  
Noisy Measurements ◽  
Theoretical Results

We consider consensus problems of first-order multiagent systems with sampled information and noisy measurements. A distributed stochastic approximation type algorithm is employed to attenuate the measurement noises. We provide conditions under which almost sure strong consensus is guaranteed for fixed and switching directed network topologies. Simulation results are provided to illustrate the theoretical results.

scholarly journals Consensus of Multi-Integral Fractional-Order Multiagent Systems with Nonuniform Time-Delays

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-24 ◽  
Author(s):  
Jun Liu ◽  
Wei Chen ◽  
Kaiyu Qin ◽  
Ping Li
Keyword(s):  
Numerical Simulations ◽  
Frequency Domain ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Multiple Integral ◽  
Frequency Domain Method ◽  
Double Integral ◽  
Single Integral ◽  
Special Case

Consensus of fractional-order multiagent systems (FOMASs) with single integral has been wildly studied. However, the dynamics with multiple integral (especially double integral to sextuple integral) also exist in FOMASs, and they are rarely studied at present. In this paper, consensus problems for multi-integral fractional-order multiagent systems (MIFOMASs) with nonuniform time-delays are addressed. The consensus conditions for MIFOMASs are obtained by a novel frequency-domain method which properly eliminates consensus problems of the systems associated with nonuniform time-delays. Besides, the method revealed in this paper is applicable to classical high-order multiagent systems which is a special case of MIFOMASs. Finally, several numerical simulations with different parameters are performed to validate the correctness of the results.

scholarly journals Collaboration Control of Fractional-Order Multiagent Systems with Sampling Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hong-yong Yang ◽  
Lei Guo ◽  
Banghai Xu ◽  
Jian-zhong Gu
Keyword(s):  
Multiagent Systems ◽  
Fractional Order ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Sampled Data ◽  
Derivative Operator ◽  
Collaborative Control ◽  
Data Control ◽  
Theoretical Results

Because of the complexity of the practical environments, many distributed multiagent systems cannot be illustrated with the integer-order dynamics and can only be described with the fractional-order dynamics. In this paper, collaboration control problems of continuous-time networked fractional-order multiagent systems via sampled control and sampling delay are investigated. Firstly, the sampled-data control of multiagent systems with fractional-order derivative operator is analyzed in a directed weighted network ignoring sampling delay. Then, the collaborative control of fractional-order multiagent systems with sampled data and sampling delay is studied in a directed and symmetrical network. Many sufficient conditions for reaching consensus with sampled data and sampling delay are obtained. Some numerical simulations are presented to illustrate the utility of our theoretical results.

Fractional Order Proportional Derivative (FOPD) and FO[PD] Controller Design for Networked Position Servo Systems

2009 ◽  
Author(s):  
Yongshun Jin ◽  
YangQuan Chen ◽  
Chunyang Wang ◽  
Ying Luo
Keyword(s):  
Fractional Order ◽  
Controller Design ◽  
Phase Margin ◽  
Crossover Frequency ◽  
Pd Controller ◽  
Servo Systems ◽  
Integer Order ◽  
Simulation Results ◽  
Position Servo ◽  
The Given

This paper considers the fractional order proportional derivative (FOPD) controller and fractional order [proportional derivative] (FO[PD]) controller for networked position servo systems. The systematic design schemes of the networked position servo system with a time delay are presented. It follows from the Bode plot of the FOPD system and the FO[PD] that the given gain crossover frequency and phase margin are fulfilled. Moreover, the phase derivative w.r.t. the frequency is zero, which means that the closed-loop system is robust to gain variations at the given gain crossover frequency. However, sometimes we can not get the controller parameters to meet our robustness requirement. In this paper, we have studied on this situation and presented the requirement of the gain cross frequency, and phase margin in the designing process. For the comparison of fractional order controllers with traditional integer order controller, the integer order proportional integral differential (IOPID) was also designed by using the same proposed method. The simulation results have verified that FOPD and FO[PD] are effective for networked position servo. The simulation results also reveal that both FOPD controller and FO[PD] controller outperform IO-PID controller for this type of system.

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