Cluster Tracking Performance Analysis of Linear Heterogeneous Multi-Agent Networks: A Complex Frequency Domain Approach

This paper presents a complex frequency domain approach to investigate the cluster tracking performance of linear heterogeneous multi-agent networks. Firstly, a designed graph matrix is given to eliminate the interaction influence between coupled subnetworks with different tracking signals. On this basis, the cluster tracking performance analysis problem is decomposed into two parts, i.e., stability analysis and steady-state performance analysis of multi-agent networks. Secondly, based on the network structure, a minimum separable subgraph set is proposed to transform the stability of the multi-agent network into the stability of the separable subnetworks. Further, a signal flow diagram is introduced to solve the stability of the separable subnetworks. Thirdly, in view of Final-value theorem, a necessary and sufficient condition is proposed for achieving the cluster tracking control for the closed-loop stable multi-agent network. This result provides a strong theoretical basis for the flexible design of controllers due to that it quantitatively reveals the inherent law of steady-state performance for multi-agent networks. Finally, an algorithm is established to calculate the steady-state error of a general directed multi-agent network. Some simulations are provided to demonstrate the effectiveness of the theoretical results.

[1]  Tianping Chen,et al.  Cluster Consensus in Discrete-Time Networks of Multiagents With Inter-Cluster Nonidentical Inputs , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Yang Shi,et al.  Consensus for Linear Multiagent Systems With Time-Varying Delays: A Frequency Domain Perspective , 2017, IEEE Transactions on Cybernetics.

[3]  Bo Sun,et al.  Disturbance observer-based control for consensus tracking of multi-agent systems with input delays from a frequency domain perspective , 2018, Syst. Control. Lett..

[4]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[5]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[6]  Sourav Bhowmick,et al.  Leader–Follower Bipartite Consensus of Uncertain Linear Multiagent Systems With External Bounded Disturbances Over Signed Directed Graph , 2019, IEEE Control Systems Letters.

[7]  Ya-Jun Pan,et al.  Distributed cooperative control of leader-follower multi-agent systems under packet dropouts for quadcopters , 2017, Syst. Control. Lett..

[8]  Jinde Cao,et al.  Exponential Consensus of Multiagent Systems With Lipschitz Nonlinearities Using Sampled-Data Information , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[10]  Zhengtao Ding,et al.  Distributed adaptive consensus and output tracking of unknown linear systems on directed graphs , 2015, Autom..

[11]  Zhong-Ping Jiang,et al.  Distributed formation control of nonholonomic mobile robots without global position measurements , 2013, Autom..

[12]  Honghai Wang,et al.  Multi-tracking control of heterogeneous multi-agent systems with single-input– single-output based on complex frequency domain analysis , 2016 .

[13]  Wei Xing Zheng,et al.  Cluster Synchronization for Interacting Clusters of Nonidentical Nodes via Intermittent Pinning Control , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Wei Xing Zheng,et al.  Adaptive Fault-Tolerant Consensus for a Class of Uncertain Nonlinear Second-Order Multi-Agent Systems With Circuit Implementation , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[16]  Richard M. Murray,et al.  INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS , 2002 .

[17]  Ya-Jun Pan,et al.  Event-Triggered Control for Consensus Problem in Multi-Agent Systems With Quantized Relative State Measurements and External Disturbance , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Changbin Yu,et al.  Consensus control of linear multi-agent systems under directed dynamic topology , 2013, 2013 European Control Conference (ECC).

[19]  Guanghui Wen,et al.  Finite-Time Bipartite Consensus for Multi-Agent Systems on Directed Signed Networks , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Jinde Cao,et al.  Observer Design for Tracking Consensus in Second-Order Multi-Agent Systems: Fractional Order Less Than Two , 2017, IEEE Transactions on Automatic Control.

[21]  Li De-quan,et al.  Leader-Following Consensus of Multi-Agent Systems , 2010 .

[22]  Sourav Bhowmick,et al.  Leader–Follower Bipartite Consensus of Linear Multiagent Systems Over a Signed Directed Graph , 2019, IEEE Transactions on Circuits and Systems II: Express Briefs.

[23]  Peng Shi,et al.  Cooperative Control of Multi-Agent Systems With Unknown State-Dependent Controlling Effects , 2015, IEEE Transactions on Automation Science and Engineering.

[24]  Sourav Bhowmick,et al.  Lag‐bipartite consensus of linear multiagent systems under saturating input over signed graph , 2019, IET Control Theory & Applications.

[25]  Xin-Ping Guan,et al.  A new framework of consensus protocol design for complex multi-agent systems , 2011, Syst. Control. Lett..

[26]  Gang Feng,et al.  Impulsive Multiconsensus of Second-Order Multiagent Networks Using Sampled Position Data , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[27]  P. Shi,et al.  Observer‐based leader‐following consensus of uncertain nonlinear multi‐agent systems , 2017 .

[28]  Yunpeng Wang,et al.  On Convergence Rate of Leader-Following Consensus of Linear Multi-Agent Systems With Communication Noises , 2015, IEEE Transactions on Automatic Control.

[29]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

[30]  Guoqiang Hu,et al.  Time-Varying Formation Tracking for Linear Multiagent Systems With Multiple Leaders , 2017, IEEE Transactions on Automatic Control.

[31]  Xiwei Liu,et al.  Cluster Synchronization in Directed Networks Via Intermittent Pinning Control , 2011, IEEE Transactions on Neural Networks.

[32]  Zhang Ren,et al.  Time-Varying Formation Tracking for Second-Order Multi-Agent Systems Subjected to Switching Topologies With Application to Quadrotor Formation Flying , 2017, IEEE Transactions on Industrial Electronics.

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

[34]  Yang Tang,et al.  Event-Triggering Containment Control for a Class of Multi-Agent Networks With Fixed and Switching Topologies , 2017, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[36]  Fuad E. Alsaadi,et al.  Event-Based Consensus for a Class of Nonlinear Multi-Agent Systems With Sequentially Connected Topology , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[37]  Wenwu Yu,et al.  An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination , 2012, IEEE Transactions on Industrial Informatics.