A Discontinuous Consensus Algorithm with Neighbor Counting

A cooperative consensus algorithm is proposed for a group of double integrators. This algorithm is based on minimal relative information and does not use communication networks. Each agent counts the number of predecessor and successor neighbors. The difference of these numbers is used in the controller instead of any accurate range or position measurements. Non-smooth Lyapunov method is used to analyze the stability under the proposed consensus algorithm. Under certain conditions, the proposed protocol can ensure bounded control input, finite-time convergence, or fixed-time convergence. Simulation results illustrate the effectiveness of the proposed algorithm.

[1]  Xu Wang,et al.  Necessary and Sufficient Conditions for Consensus of Double-Integrator Multi-Agent Systems With Measurement Noises , 2011, IEEE Transactions on Automatic Control.

[2]  Arijit Sen,et al.  Cooperative formation control strategy in heterogeneous network with bounded acceleration , 2017, 2017 Indian Control Conference (ICC).

[3]  Arijit Sen,et al.  Cooperative Target-centric Formation Control without Relative Velocity Measurements under Heterogeneous Networks , 2017, J. Intell. Robotic Syst..

[4]  S. Bhat,et al.  Finite-time semistability, Filippov systems, and consensus protocols for nonlinear dynamical networks with switching topologies , 2010 .

[5]  Alessandro Astolfi,et al.  Homogeneous Approximation, Recursive Observer Design, and Output Feedback , 2008, SIAM J. Control. Optim..

[6]  Sandeep Anand,et al.  Distributed secondary control with reduced communication in low-voltage DC microgrid , 2016, 2016 10th International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG).

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

[8]  J. Cortés.  Discontinuous dynamical systems , 2008, IEEE Control Systems.

[9]  Wenwu Yu,et al.  Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems , 2010, Autom..

[10]  Yu. S. Ledyaev,et al.  Nonsmooth analysis and control theory , 1998 .

[11]  Guanghui Wen,et al.  Designing Distributed Specified-Time Consensus Protocols for Linear Multiagent Systems Over Directed Graphs , 2019, IEEE Transactions on Automatic Control.

[12]  Guanghui Wen,et al.  Finite-time consensus for second-order multi-agent systems with saturated control protocols , 2015 .

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

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

[15]  Abdelkader Abdessameud,et al.  On consensus algorithms design for double integrator dynamics , 2013, Autom..

[16]  Sergey Parsegov,et al.  Fixed-time consensus algorithm for multi-agent systems with integrator dynamics , 2013 .

[17]  Xinping Guan,et al.  Flocking for multi-agent systems with optimally rigid topology based on information weighted Kalman consensus filter , 2017 .

[18]  Yigang He,et al.  Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Lu Liu,et al.  Cooperative Output Regulation of Heterogeneous Linear Multi-Agent Systems by Event-Triggered Control , 2017, IEEE Transactions on Cybernetics.

[20]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[21]  Wei Ren.  On Consensus Algorithms for Double-Integrator Dynamics , 2008, IEEE Trans. Autom. Control..

[22]  Sandeep Anand,et al.  Quality-Index Based Distributed Secondary Controller for a Low-Voltage DC Microgrid , 2018, IEEE Transactions on Industrial Electronics.

[23]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[24]  Abdelkader Abdessameud,et al.  Distributed Consensus Algorithms for a Class of High-Order Multi-Agent Systems on Directed Graphs , 2018, IEEE Transactions on Automatic Control.

[25]  Yiguang Hong,et al.  Finite-Time Consensus for Multi-Agent Networks with Second-Order Agent Dynamics , 2008 .

[26]  P. Olver.  Nonlinear Systems , 2013 .

[27]  Dennis S. Bernstein,et al.  Geometric homogeneity with applications to finite-time stability , 2005, Math. Control. Signals Syst..

[28]  Zhengtao Ding,et al.  Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics , 2018, IEEE Transactions on Automatic Control.

[29]  Arijit Sen,et al.  Nonlinear formation control strategies for agents without relative measurements under heterogeneous networks , 2018 .

[30]  A. Bacciotti,et al.  Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions , 1999 .

[31]  Ravi N. Banavar,et al.  Rendezvous in space with minimal sensing and coarse actuation , 2013, Autom..