A novel consensus algorithm for second‐order multi‐agent systems without velocity measurements

In this paper, a novel consensus protocol for second‐order multi‐agent systems is elegantly designed, and it relaxes the common requirement of the velocity information of the agents. An interesting consensus criterion is explicitly derived in terms of the proposed cooperation law provided that the dynamical equation for each agent is linear. As an extension, the proposed cooperation rule is further extended to a general scenario, where the coupling weights characterizing the relationships among the neighboring agents are time‐varying. Accordingly, two distributed cooperative algorithms (node/edge‐based scheme) are explicitly designed. Moreover, we study the case of network with switching communication setting. It shows that edge‐based law is capable with the time‐varying topology, while the node‐based scheme is not. In addition, the proposed coordination strategies are applied to the tracking problem as well. Finally, these obtained consensus results are well supported in the light of the pendulum models. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  M. Marden.  Geometry of Polynomials , 1970 .

[2]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[3]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[4]  Francesco Bullo,et al.  Coordination and Geometric Optimization via Distributed Dynamical Systems , 2003, SIAM J. Control. Optim..

[5]  Stephen P. Boyd,et al.  Randomized gossip algorithms , 2006, IEEE Transactions on Information Theory.

[6]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[7]  Ella M. Atkins,et al.  Distributed multi‐vehicle coordinated control via local information exchange , 2007 .

[8]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[9]  Jinde Cao,et al.  Adaptive synchronization of uncertain dynamical networks with delayed coupling , 2008 .

[10]  F. Garofalo,et al.  Synchronization of complex networks through local adaptive coupling. , 2008, Chaos.

[11]  Jinde Cao,et al.  Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[12]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[13]  Wenwu Yu,et al.  Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  Daniel W. C. Ho,et al.  Globally Exponential Synchronization and Synchronizability for General Dynamical Networks , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Yu-Ping Tian,et al.  Consensus of Data-Sampled Multi-Agent Systems With Random Communication Delay and Packet Loss , 2010, IEEE Transactions on Automatic Control.

[16]  Jinde Cao,et al.  Second-order consensus in multi-agent dynamical systems with sampled position data , 2011, Autom..

[17]  D. Ho,et al.  Stabilization of complex dynamical networks with noise disturbance under performance constraint , 2011 .

[18]  Jinde Cao,et al.  Pinning impulsive stabilization of nonlinear Dynamical Networks with Time-Varying Delay , 2012, Int. J. Bifurc. Chaos.

[19]  Panos Louvieris,et al.  Robust Synchronization for 2-D Discrete-Time Coupled Dynamical Networks , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[20]  K. Yıldırım.  CLOCK SYNCHRONIZATION IN WIRELESS SENSOR NETWORKS , 2012 .

[21]  Tingwen Huang,et al.  Second-Order Locally Dynamical Consensus of Multiagent Systems With Arbitrarily Fast Switching Directed Topologies , 2013, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[22]  Gang Feng,et al.  Containment control of linear multi‐agent systems with multiple leaders of bounded inputs using distributed continuous controllers , 2013, ArXiv.

[23]  Tingwen Huang,et al.  Second-Order Consensus Seeking in Multi-Agent Systems With Nonlinear Dynamics Over Random Switching Directed Networks , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Wei Ren,et al.  Distributed consensus of linear multi-agent systems with adaptive dynamic protocols , 2011, Autom..

[25]  Wei Xing Zheng,et al.  Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics , 2013, Autom..

[26]  Guanrong Chen,et al.  Problems and Challenges in Control Theory under Complex Dynamical Network Environments , 2013 .

[27]  Daniel W. C. Ho,et al.  A Unified Approach to Practical Consensus with Quantized Data and Time Delay , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Guangfu Ma,et al.  Distributed coordination for second-order multi-agent systems with nonlinear dynamics using only relative position measurements , 2013, Autom..

[29]  Guang-Ren Duan,et al.  Gain Scheduled Control of Linear Systems Subject to Actuator Saturation With Application to Spacecraft Rendezvous , 2014, IEEE Transactions on Control Systems Technology.

[30]  Yang Liu,et al.  Distributed consensus for sampled-data control multi-agent systems with missing control inputs , 2014, Appl. Math. Comput..

[31]  Jorge Cortes,et al.  Dynamic average consensus under limited control authority and privacy requirements , 2014, 1401.6463.

[32]  Huijun Gao,et al.  Coordination for Linear Multiagent Systems With Dynamic Interaction Topology in the Leader-Following Framework , 2014, IEEE Transactions on Industrial Electronics.

[33]  Huijun Gao,et al.  Pinning Distributed Synchronization of Stochastic Dynamical Networks: A Mixed Optimization Approach , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[34]  Jinde Cao,et al.  Synchronization in an Array of Output-Coupled Boolean Networks With Time Delay , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Huijun Gao,et al.  Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses , 2015, Autom..

[36]  Tingwen Huang,et al.  Event-Triggering Sampling Based Leader-Following Consensus in Second-Order Multi-Agent Systems , 2015, IEEE Transactions on Automatic Control.

[37]  David J. Hill,et al.  Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks , 2015, Neural Networks.

[38]  Jinde Cao,et al.  Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers , 2015, J. Frankl. Inst..

[39]  Tingwen Huang,et al.  Second-Order Global Consensus in Multiagent Networks With Random Directional Link Failure , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[40]  Yang Liu,et al.  Feedback Controller Design for the Synchronization of Boolean Control Networks , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[41]  Yang Liu,et al.  Observer based consensus for nonlinear multi-agent systems with communication failures , 2016, Neurocomputing.

[42]  Guanghui Wen,et al.  Distributed node‐to‐node consensus of multi‐agent systems with stochastic sampling , 2016 .

[43]  Yang Liu,et al.  Observer-based distributed consensus for general nonlinear multi-agent systems with interval control inputs , 2016, Int. J. Control.

[44]  Yang Cao,et al.  Observer-Based Consensus Tracking of Nonlinear Agents in Hybrid Varying Directed Topology , 2017, IEEE Transactions on Cybernetics.