Preserving Stability Under Communication Delays in Multi Agent Systems

2013 ◽  
Author(s):  
Hossein Rastgoftar ◽  
Suhada Jayasuriya
Keyword(s):  
Time Delays ◽  
Communication Delays ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Continuum Approach ◽  
Position Information ◽  
Characteristic Roots ◽  
Multi Agent ◽  
Velocity Information ◽  
The Stability

The effect of time delays on the stability of a recently proposed continuum approach for controlling a multi agent system (MAS) evolving in n-D under a special local inter-agent communication protocol is considered. There a homogenous map determined by n+1 leaders is learned by the follower agents each communicating with n+1 adjacent agents. In this work both position and velocity information of adjacent agents are used for local control of follower agents whereas in previous work [1, 2] only position information of adjacent agents was used. Stability of the proposed method under a time delay h is studied using the cluster treatment of characteristic roots (CTCR) [3]. It is shown that the stability of MAS evolution can be preserved when (i) the velocity of any follower agent is updated using both position and velocity of its adjacent agents at time (t-h); and (ii) the communication matrix has real eigenvalues. In addition, it is shown that when there is no communication delay, deviations from a selected homogenous map during transients may be minimized by updating only the position of a follower using both position and velocity of its adjacent agents.

Stability of a Consensus Protocol for Second Order Agents With Multiple Time Delays

2011 ◽  
Author(s):  
Rudy Cepeda-Gomez ◽  
Nejat Olgac
Keyword(s):  
Information Exchange ◽  
Time Delays ◽  
Second Order ◽  
Multiple Time ◽  
State Transformation ◽  
Consensus Protocol ◽  
Position Information ◽  
Characteristic Roots ◽  
Velocity Information ◽  
The Stability

In this study we consider the consensus problem for a group of second order agents interacting under a fixed, undirected communication topology. Communication lines are affected by two rationally independent delays. The first delay is assumed to be in the position information channels whereas the second one is in the velocity information exchange. The delays are assumed to be uniform throughout the entire network. We first reduce the complexity of the problem, by performing a state transformation that allows the decomposition of the characteristic equation of the system into a set of second order factors. The stability of the resulting subsystems is analyzed exactly and exhaustively in the domain of the time delays using the Cluster Treatment of Characteristic Roots (CTCR) paradigm. CTCR is a recent method which declares the stability features of the system for any composition of the time delays. Example cases are provided to verify the analytical conclusions.

Reduced-order observer-based consensus control of linear multi-agent systems over directed networks with nonuniform communication delays

2020 ◽  
pp. 014233122093430
Author(s):  
Qiuzhen Wang ◽  
Jiangping Hu ◽  
Yiyi Zhao ◽  
Bijoy Kumar Ghosh
Keyword(s):  
Time Varying ◽  
Communication Delays ◽  
Multi Agent Systems ◽  
Consensus Control ◽  
Reduced Order ◽  
Reduced Order Observer ◽  
Multi Agent ◽  
The Stability ◽  
Output Information ◽  
Theoretical Results

This paper considers a consensus control of a general linear multi-agent system with time-varying communication delays. Since each agent can only use the relative output information from its neighbors, a reduced-order observer-based control protocol is proposed to guarantee consensus on the directed communication network. The stability of the closed-loop system is analyzed for the cases with uniform delays and nonuniform time-varying delays, respectively. Moreover, the upper bounds of the communication delays are obtained respectively for the two cases. Finally, two numerical examples are provided to illustrate the proposed theoretical results.

scholarly journals A Lyapunov–Krasovskii Functional Approach to Stability and Linear Feedback Synchronization Control for Nonlinear Multi-Agent Systems with Mixed Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
A. Stephen ◽  
R. Raja ◽  
J. Alzabut ◽  
Q. Zhu ◽  
M. Niezabitowski ◽  
...  
Keyword(s):  
Time Delays ◽  
Analytical Techniques ◽  
Linear Feedback ◽  
Synchronization Control ◽  
Multi Agent Systems ◽  
Feedback Controllers ◽  
Agent Systems ◽  
Mixed Time Delays ◽  
Multi Agent ◽  
The Stability

This study focuses on mixed time delayed, both leaderless and leader-follower problems of nonlinear multi-agent systems. Here, we find the stability criteria for multi-agent systems (MASs) by utilizing a proposed lemma, the Lyapunov–Krasovskii functions, analytical techniques, Kronecker product, and some general specifications to obtain the asymptotic stability for the constructed MASs. Furthermore, the criteria to establish the synchronization of leader-follower multiagent systems with linear feedback controllers are discussed. Finally, we provide two numerical calculations along with the computational simulations to check the validity of the theoretical findings reported for both leaderless and leader-follower problem in this study.

scholarly journals Stability Analysis of a Predecessor-Following Platoon of Vehicles With Two Time Delays

2015 ◽  
Vol 27 (1) ◽  
pp. 35-46 ◽  
Author(s):  
Ali Ghasemi ◽  
Saeed Rouhi
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Disturbance Attenuation ◽  
One Dimension ◽  
String Stability ◽  
Characteristic Roots ◽  
Vehicle Platoon ◽  
Velocity Information ◽  
The Stability ◽  
Lead Vehicle

The problem of controlling a platoon of vehicles moving in one dimension is considered so that they all follow a lead vehicle with constant spacing between successive vehicles. The stability and the string stability of a platoon of vehicles with two independent and uncertain delays, one in the inter-vehicle distance and the other in the relative velocity information channels, are considered. The main objectives of this paper are: (1) using a simplifying factorization procedure and deploying the cluster treatment of characteristic roots (CTCR) paradigm to obtain exact stability boundaries in the domain of the delays, and (2) for the purpose of disturbance attenuation, the string stability analysis is examined. Finally, a simulation example of multiple vehicle platoon control is used to demonstrate the effectiveness of the proposed method.

Swarm Motion as Particles of a Continuum With Communication Delays

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Hossein Rastgoftar ◽  
Suhada Jayasuriya
Keyword(s):  
Time Delay ◽  
Formation Control ◽  
Communication Delay ◽  
Multi Agent Systems ◽  
Local Communication ◽  
Agent Systems ◽  
Characteristic Roots ◽  
Multi Agent ◽  
Homogeneous Map ◽  
The Stability

In this paper, we give an upper bound for the communication delay in a multi-agent system (MAS) that evolves under a recently developed continuum paradigm for formation control. The MAS is treated as particles of a continuum that transforms under special homeomorphic mapping, called a homogeneous map. Evolution of an MAS in ℝn is achieved under a special communication topology proposed by Rastgoftar and Jayasuriya (2014, “Evolution of Multi Agent Systems as Continua,” ASME J. Dyn. Syst. Meas. Control, 136(4), p. 041014) and (2014, “An Alignment Strategy for Evolution of Multi Agent Systems,” ASME J. Dyn. Syst. Meas. Control, 137(2), p. 021009), employing a homogeneous map specified by the trajectories of n+1 leader agents at the vertices of a polytope in ℝn, called the leading polytope. The followers that are positioned in the convex hull of the leading polytope learn the prescribed homogeneous mapping through local communication with neighboring agents using a set of communication weights prescribed by the initial positions of the agents. However, due to inevitable time-delay in getting positions and velocities of the adjacent agents through local communication, the position of each follower may not converge to the desired state given by the homogeneous map leaving the possibility that MAS evolution may get destabilized. Therefore, ascertaining the stability under time-delay is important. Stability analysis of an MAS consisting of a large number of agents, leading to higher-order dynamics, using conventional methods such as cluster treatment of characteristic roots (CTCR) or Lyapunov–Krasovskii are difficult. Instead we estimate the maximum allowable communication delay for the followers using one of the eigenvalues of the communication matrix that places MAS evolution at the margin of instability. The proposed method is advantageous because the transcendental delay terms are directly used and the characteristic equation of MAS evolution is not approximated by a finite-order polynomial. Finally, the developed framework is used to validate the effect of time-delays in our previous work.

scholarly journals Flocking for Multiagent Systems with Partial Information Exchange Based on Inclusion Principle

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hui Wei ◽  
Xuebo Chen
Keyword(s):  
Information Exchange ◽  
Partial Information ◽  
Individual Heterogeneity ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
The Stability ◽  
The Individual ◽  
Multi Agents

This paper investigates the flocking problem of multi-agents with partial information exchange, which means that only part, but not all, of the agents are informed of the group objective. A distributed flocking model based on the inclusion principle is provided to simplify the design and analysis of multi-agent systems. Furthermore, to reduce the communication energy consumption, an improved flocking algorithm based on the model is proposed to achieve stable flocking for all the agents. The stability of the multi-agent system is then established, with the help of the Lyapunov stability theorem and LaSalle’s invariance principle. Especially, considering the individual heterogeneity in both nature and engineering applications, we also investigate the flocking problem of multi-agents with different sensing radiuses and equilibrium distances. Finally, two kinds of simulation results are presented to demonstrate the validity of the proposed results. This work provides an insight not only into the properties of the different species of individual flocking, but also into the theoretical framework for the engineering design of multi-agent systems considering individual heterogeneity.

scholarly journals Distributed Adaptive Formation Tracking Control under Fixed and Switching Topologies: Application on General Linear Multi-Agent Systems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 941
Author(s):  
Tianhao Sun ◽  
Huiying Liu ◽  
Yongming Yao ◽  
Tianyu Li ◽  
Zhibo Cheng
Keyword(s):  
Switching Topology ◽  
General Linear ◽  
Time Varying ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Agent System ◽  
Switching Topologies ◽  
Formation Tracking ◽  
Leader Following ◽  
Multi Agent

In this paper, the time-varying formation tracking problem of the general linear multi-agent system is discussed. A distributed formation tracking protocol based on Riccati inequalities with adaptive coupling weights among the follower agents and the leader agent is designed for a leader-following multi-agent system under fixed and switching topologies. The formation configuration involved in this paper is expressed as a bounded piecewise continuously differentiable vector function. The follower agents will achieve the desired formation tracking trajectory of the leader. In traditional static protocols, the coupling weights depend on the communication topology and is a constant. However, in this paper, the coupling weights are updated by the state errors among the neighboring agents. Moreover, the stability analysis of the MAS under switching topology is presented, and proves that the followers also could achieve pre-specified time-varying formation, if the communication graph is jointly connected. Two numerical simulations indicate the capabilities of the algorithms.

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