Consensus Analysis and Formation Control of Second-Order Multiagent Systems Via Nonlinear Protocol

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Huan Pan ◽  
Xiaohong Nian ◽  
Ling Guo
Keyword(s):  
Multiagent Systems ◽  
Invariance Principle ◽  
Control Strategy ◽  
Formation Control ◽  
Multiagent System ◽  
Sufficient Conditions ◽  
Second Order ◽  
General Linear ◽  
Communication Graph ◽  
Consensus Analysis

This paper mainly investigates consensus and formation control of second-order multiagent system with undirected communication graph. A nonlinear protocol is proposed as an extension of general linear protocols that have been widely studied. In order to achieve formation control, a formation control strategy corresponding to the nonlinear protocol is designed too. The sufficient conditions of consensus and formation are derived based on LaSalle's invariance principle. Simulation examples are provided to illustrate that the second-order multiagent with the nonlinear protocol can achieve consensus and formation.

scholarly journals Second-Order Consensus in Multiagent Systems via Nonlinear Protocol

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Huan Pan ◽  
Xiaohong Nian ◽  
Ling Guo
Keyword(s):  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Invariance Principle ◽  
Lyapunov Functions ◽  
Multiagent System ◽  
Second Order ◽  
General Linear ◽  
Reference Velocity ◽  
Communication Topology ◽  
Lasalle's Invariance Principle

This paper focuses on theoretical analysis of second-order consensus in multiagent system. As an extension of the general linear protocol, a nonlinear protocol is designed for multiagent system with undirected communication topology. The nonlinear protocol is also applied to achieve reference velocity consensus. Through choosing the appropriate Lyapunov functions and using LaSalle’s invariance principle, some consensus conditions are derived. Simulation examples are provided to demonstrate the effectiveness of the proposed results.

scholarly journals Observer-Based Event-Triggered Circle Formation Control for First- and Second-Order Multiagent Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Peng Xu ◽  
Guangming Xie ◽  
Jin Tao ◽  
Minyi Xu ◽  
Quan Zhou
Keyword(s):  
Multiagent Systems ◽  
Measurement Errors ◽  
Formation Control ◽  
Sufficient Conditions ◽  
Second Order ◽  
State Function ◽  
Control Laws ◽  
Interevent Interval ◽  
Circle Formation ◽  
Event Triggered

This paper proposes an observer-based event-triggered algorithm to solve circle formation control problems for both first- and second-order multiagent systems, where the communication topology is modeled by a spanning tree-based directed graph with limited resources. In particular, the observation-based event-triggering mechanism is used to reduce the update frequency of the controller, and the triggering time depends on the norm of the state function and the trigger threshold of measurement errors. The analysis shows that sufficient conditions are established for achieving the desired circle formation, while there exists at least one agent for which the next interevent interval is strictly positive. Numerical simulations of both first- and second-order multiagent systems are also given to demonstrate the effectiveness of the proposed control laws.

scholarly journals Eigenvalue Based Approach for Global Consensus in Multiagent Systems with Nonlinear Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Wei Qian ◽  
Lei Wang
Keyword(s):  
Nonlinear Dynamics ◽  
Multiagent Systems ◽  
Multiagent System ◽  
Symmetric Matrix ◽  
Algebraic Connectivity ◽  
Communication Graph ◽  
Consensus Protocol ◽  
Global Consensus ◽  
The Common ◽  
Analytical Result

This paper addresses the global consensus of nonlinear multiagent systems with asymmetrically coupled identical agents. By employing a Lyapunov function and graph theory, a sufficient condition is presented for the global exponential consensus of the multiagent system. The analytical result shows that, for a weakly connected communication graph, the algebraic connectivity of a redefined symmetric matrix associated with the directed graph is used to evaluate the global consensus of the multiagent system with nonlinear dynamics under the common linear consensus protocol. The presented condition is quite simple and easily verified, which can be effectively used to design consensus protocols of various weighted and directed communications. A numerical simulation is also given to show the effectiveness of the analytical result.

scholarly journals Distributed Consensus Tracking for Second-Order Nonlinear Multiagent Systems with a Specified Reference State

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Guoguang Wen ◽  
Yongguang Yu ◽  
Zhaoxia Peng ◽  
Ahmed Rahmani
Keyword(s):  
Multiagent Systems ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lyapunov Theory ◽  
Reference Trajectory ◽  
Distributed Consensus ◽  
Consensus Tracking ◽  
Velocity Information ◽  
Virtual Leader

This paper mainly addresses the distributed consensus tracking problem for second-order nonlinear multiagent systems with a specified reference trajectory. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position and velocity information of its neighbors. The consensus reference is taken as a virtual leader, whose output is only its position and velocity information that is available to only a subset of a group of followers. To achieve consensus tracking, a class of nonsmooth control protocols is proposed which reply on the relative information among the neighboring agents. Then some corresponding sufficient conditions are derived. It is shown that if the communication graph associated with the virtual leader and followers is connected at each time instant, the consensus can be achieved at least globally exponentially with the proposed protocol. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Finally, numerical examples are presented to illustrate the theoretical analysis.

scholarly journals Consensus Analysis of High-Order Multiagent Systems with General Topology and Asymmetric Time-Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Fangcui Jiang
Keyword(s):  
Multiagent Systems ◽  
Network Topology ◽  
Time Delays ◽  
Multiagent System ◽  
High Order ◽  
Directed Network ◽  
Time Varying ◽  
Consensus Analysis ◽  
Robust Consensus ◽  
Selection Of

This paper focuses on the consensus problem for high-order multiagent systems (MAS) with directed network and asymmetric time-varying time-delays. It is proved that the high-order multiagent system can reach consensus when the network topology contains a spanning tree and time-delay is bounded. The main contribution of this paper is that a Lyapunov-like design framework for the explicit selection of protocol parameters is provided. The Lyapunov-like design guarantees the robust consensus of the high-order multiagent system with respect to asymmetric time-delays and is independent of the exact knowledge of the topology when the communication linkages among agents are undirected and connected.

Time-Varying Formation Control for Time-Delayed Multi-Agent Systems with General Linear Dynamics and Switching Topologies

2019 ◽  
Vol 07 (01) ◽  
pp. 3-13 ◽  
Author(s):  
Wei Xiao ◽  
Jianglong Yu ◽  
Rui Wang ◽  
Xiwang Dong ◽  
Qingdong Li ◽  
...  
Keyword(s):  
Formation Control ◽  
Sufficient Conditions ◽  
General Linear ◽  
Time Varying ◽  
Multi Agent Systems ◽  
Analysis And Design ◽  
Agent Systems ◽  
Control Protocol ◽  
Switching Topologies ◽  
Multi Agent

Time-varying formation analysis and design problems for general linear multi-agent systems with switching interaction topologies and time-varying delays are studied. Firstly, a consensus-based formation control protocol is constructed using local information of the neighboring agents. An algorithm with three steps is presented to design the proposed formation control protocol. Then, based on linear matrix inequality technique and common Lyapunove–Krasovskii stability theory, sufficient conditions for general linear multi-agent systems with switching topologies and time-varying delays to achieve time-varying formation are given together with a time-varying formation feasibility condition. Finally, a numerical simulation is given to demonstrate the effectiveness of the obtained theoretical results.

scholarly journals Energy-Limited Time-Varying Formation Control for Second-Order Multiagent Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Wanzhen Quan ◽  
Yulong Zhao ◽  
Le Wang ◽  
Xiaogang Yang
Keyword(s):  
Control Problem ◽  
Total Energy ◽  
Multiagent Systems ◽  
Formation Control ◽  
Orthogonal Transformation ◽  
Second Order ◽  
Time Varying ◽  
Limited Time ◽  
Leader Following ◽  
Energy Limitation

The energy-limited time-varying formation (ETVF) control problem of second-order multiagent systems (MAS) is addressed for both leaderless and leader-following communication topologies in this paper. Different from the previous results, the joint consideration of energy limitation and formation design is more challenging and practical. First, an ETVF control protocol is presented, and the total energy supply is pregiven and limited, which is more common in practical applications. Then, by an orthogonal transformation, the formation control problem is converted into the consensus stabilization problem for second-order leaderless MAS, where sufficient conditions for the ETVF are derived by joint design of control gains and the total energy. At the same time, the explicit formula that forms the formation center function is obtained to depict the macroscopic movement of the multiagent system as a whole. Moreover, the proposed method is also extended to the leader-following communication structure. Finally, two examples are given to verify the effectiveness of our theoretical results.

scholarly journals Consensus Analysis for a Class of Heterogeneous Multiagent Systems with Time Delay Based on Frequency Domain Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yi-Jie Sun ◽  
Guo-liang Zhang ◽  
Jing Zeng
Keyword(s):  
Time Delay ◽  
Frequency Domain ◽  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Frequency Domain Method ◽  
Consensus Protocol ◽  
Consensus Analysis ◽  
Domain Method ◽  
Communication Topology ◽  
System Coupling

The consensus problem of heterogeneous multiagent systems composed of first-order and second-order agent is investigated. A linear consensus protocol is proposed. Based on frequency domain method, the sufficient conditions of achieving consensus are obtained. If communication topology contains spanning tree and some conditions can be satisfied on control gains, consensus can be achieved. Then, a linear consensus protocol with time delay is proposed. In this case, consensus is dependent only on system coupling strength, each agent input time delay, but independent of communication delay. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical result.

scholarly journals Consensus Analysis of Second-Order Multiagent Systems with General Topology and Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bo Liu ◽  
Guangming Xie ◽  
Yanping Gao ◽  
Jiaxi Wu ◽  
Jianguo Zhang ◽  
...  
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Nearest Neighbor ◽  
Laplacian Matrix ◽  
Second Order ◽  
General Topology ◽  
Consensus Analysis ◽  
Laplace Transform Technique ◽  
Eigenvalues Of The Laplacian ◽  
Nearest Neighbor Rule

This paper addresses the consensus of second-order multiagent systems with general topology and time delay based on the nearest neighbor rule. By using the Laplace transform technique, it is proved that the second-order multi-agent system in the presence of time-delay can reach consensus if the network topology contains a globally reachable node and time delay is bounded. The bound of time-delay only depends on eigenvalues of the Laplacian matrix of the system. The main contribution of this paper is that the accurate state of the consensus center and the upper bound of the communication delay to make the agents reach consensus are given. Some numerical simulations are given to illustrate the theoretical results.

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