Consensus in multi-agent systems subject to input saturation and time-varying delays

This paper deals with the problem of consensus in multi-agent systems. The consensus is investigated considering directed networks composed by identical agents described by linear models of arbitrary order, subject to input saturation and non-uniform time-varying delays. The main results are sufficient conditions for consensus analysis and design of distributed consensus protocols for multi-agent systems. In addition, because the saturation might prevent the multi-agent system to attain consensus on some set of initial conditions, it is also proposed a strategy to calculate a region in which the consensus is guaranteed. The results follow from the Lyapunov–Krasovskii theory and are formulated in the linear matrix inequalities (LMIs) framework. Finally, we present examples to illustrate the effectiveness of the proposed method in contrast with similar approaches existing in the literature.

[1]  Zi-Jiang Yang,et al.  Distributed prescribed performance control for consensus output tracking of nonlinear semi-strict feedback systems using finite-time disturbance observers , 2019, Int. J. Syst. Sci..

[2]  Pierre-Alexandre Bliman,et al.  Average consensus problems in networks of agents with delayed communications , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[3]  Chunxia Dou,et al.  Adaptive PI Control for Consensus of Multiagent Systems With Relative State Saturation Constraints , 2019, IEEE Transactions on Cybernetics.

[4]  Guangren Duan,et al.  Leader-following fixed-time output feedback consensus for second-order multi-agent systems with input saturation , 2018, Int. J. Syst. Sci..

[5]  Guoping Liu,et al.  Delay‐dependent stability and stabilization of neutral time‐delay systems , 2009 .

[6]  B. Barmish,et al.  Null Controllability of Linear Systems with Constrained Controls , 2006 .

[7]  Mohammad Javad Yazdanpanah,et al.  Finite time consensus of nonlinear multi-agent systems in the presence of communication time delays , 2020, Eur. J. Control.

[8]  Guo-Ping Liu,et al.  Consensus for heterogeneous networked multi-agent systems with switching topology and time-varying delays , 2018, J. Frankl. Inst..

[9]  Somanath Majhi,et al.  Consensus of second order multi-agents with actuator saturation and asynchronous time-delays , 2017, ArXiv.

[10]  Sophie Tarbouriech,et al.  Stability and Stabilization of Linear Systems with Saturating Actuators , 2011 .

[11]  S. Tarbouriech,et al.  Control design for linear systems with saturating actuators and /spl Lscr//sub 2/-bounded disturbances , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[12]  Maria Elena Valcher,et al.  On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions , 2014, Syst. Control. Lett..

[13]  Valter J. S. Leite,et al.  Robust Local Stabilization of Discrete-Time Systems with Time-Varying State Delay and Saturating Actuators , 2018, Mathematical Problems in Engineering.

[14]  Qi Wang,et al.  Robust finite-time consensus tracking for second-order multi-agent systems with input saturation under general directed communication graphs , 2019, Int. J. Control.

[15]  Chunxia Dou,et al.  Observer-Based Consensus of Nonlinear Multiagent Systems With Relative State Estimate Constraints , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[16]  Lixin Gao,et al.  Consensus of Lipschitz Nonlinear Multiagent Systems With Input Delay via Observer-Based Truncated Prediction Feedback , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[17]  Magnus Egerstedt,et al.  Graph Theoretic Methods in Multiagent Networks , 2010, Princeton Series in Applied Mathematics.

[18]  Tao Li,et al.  Consensus conditions of continuous-time multi-agent systems with time-delays and measurement noises , 2016, Autom..

[19]  Zhaoxia Peng,et al.  Dynamical group consensus of heterogenous multi-agent systems with input time delays , 2016, Neurocomputing.

[20]  Zengqiang Chen,et al.  Containment control for second-order nonlinear multi-agent systems with intermittent communications , 2019, Int. J. Syst. Sci..

[21]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[22]  R. Murray,et al.  Consensus protocols for networks of dynamic agents , 2003, Proceedings of the 2003 American Control Conference, 2003..

[23]  Guanrong Chen,et al.  Fully Distributed Event-Triggered Semiglobal Consensus of Multi-agent Systems With Input Saturation , 2017, IEEE Transactions on Industrial Electronics.

[24]  Long Wang,et al.  Consensus of Multi-Agent Systems in Directed Networks With Nonuniform Time-Varying Delays , 2009, IEEE Transactions on Automatic Control.

[25]  Pierre-Alexandre Bliman,et al.  Average consensus problems in networks of agents with delayed communications , 2005, CDC 2005.

[26]  Chunxia Dou,et al.  Consensus of Multiagent Systems With Time-Varying Input Delay via Truncated Predictor Feedback , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[27]  Muhammad Riaz,et al.  Consensus tracking of nonlinear multi-agent systems under input saturation with applications: A sector-based approach. , 2020, ISA transactions.

[28]  Lei Qi,et al.  Distributed formation control of fractional-order multi-agent systems with relative damping and nonuniform time-delays. , 2019, ISA transactions.

[29]  Yingmin Jia,et al.  Event-triggered consensus control for uncertain multi-agent systems with external disturbance , 2018, Int. J. Syst. Sci..

[30]  Khashayar Khorasani,et al.  Team Consensus for a Network of Unmanned Vehicles in Presence of Actuator Faults , 2010, IEEE Transactions on Control Systems Technology.

[31]  Sophie Tarbouriech,et al.  Antiwindup design with guaranteed regions of stability: an LMI-based approach , 2005, IEEE Transactions on Automatic Control.

[32]  S. Tarbouriech,et al.  Anti-windup design: an overview of some recent advances and open problems , 2009 .

[33]  Leonardo A. B. Tôrres,et al.  Consensus for double-integrator dynamics with velocity constraints , 2014 .

[34]  Karl Henrik Johansson,et al.  Distributed Event-Triggered Control for Multi-Agent Systems , 2012, IEEE Transactions on Automatic Control.

[35]  Emilia Fridman,et al.  Tutorial on Lyapunov-based methods for time-delay systems , 2014, Eur. J. Control.

[36]  Fernando de Oliveira Souza,et al.  Consensus with guaranteed convergence rate of high-order integrator agents in the presence of time-varying delays , 2016, Int. J. Syst. Sci..

[37]  Yongdo Lim,et al.  Finite-time consensus of Markov jumping multi-agent systems with time-varying actuator faults and input saturation. , 2018, ISA transactions.

[38]  Weidong Zhang,et al.  Observer-Based Consensus Control Against Actuator Faults for Linear Parameter-Varying Multiagent Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[39]  Wei Xing Zheng,et al.  Network-based practical set consensus of multi-agent systems subject to input saturation , 2018, Autom..

[40]  Carlos R. P. dos Santos,et al.  Conditions for Consensus of Multi-Agent Systems With Time-Delays and Uncertain Switching Topology , 2016, IEEE Transactions on Industrial Electronics.

[41]  Dong Yue,et al.  Consensus of Multiagent Systems With Relative State Saturations , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

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

[43]  Wei Liu,et al.  Decentralized Multi-Agent System-Based Cooperative Frequency Control for Autonomous Microgrids With Communication Constraints , 2014, IEEE Transactions on Sustainable Energy.

[44]  Guangming Xie,et al.  Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays , 2008, Syst. Control. Lett..

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

[46]  Tingshu Hu,et al.  An analysis and design method for linear systems subject to actuator saturation and disturbance , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[47]  Long Wang,et al.  Recent Advances in Consensus of Multi-Agent Systems: A Brief Survey , 2017, IEEE Transactions on Industrial Electronics.

[48]  Chunxia Dou,et al.  Consensus of Multiagent Systems With Time-Varying Input Delay and Relative State Saturation Constraints , 2020 .

[49]  Jie Ma,et al.  Semi-global leader-following coordination of multi-agent systems with input saturation and aperiodic intermittent communications , 2019, J. Frankl. Inst..

[50]  Claudio Altafini,et al.  Consensus Problems on Networks With Antagonistic Interactions , 2013, IEEE Transactions on Automatic Control.

[51]  Chuanjiang Li,et al.  Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays , 2018, International Journal of Robust and Nonlinear Control.

[52]  Dipti Srinivasan,et al.  A comparative analysis of centralized and decentralized multi-agent architecture for service restoration , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[53]  Sophie Tarbouriech,et al.  Design of Anti-Windup Compensators for a Class of Nonlinear Control Systems with Actuator Saturation , 2013 .

[54]  Eduardo Sontag.  An algebraic approach to bounded controllability of linear systems , 1984 .