Finite-time consensus control of second-order nonlinear systems with input saturation

In this paper we consider finite-time consensus control for a group of second-order systems, including double-integrator systems and nonlinear mechanical systems. Distributed controllers are designed such that a consensus is reached while all the agents in the multi-agent system suffer from input saturation. Firstly, we propose distributed controllers for multiple double-integrator systems under the leader–follower scenario while only part of the agents have access to the leader. We also assume that the velocities of the agents are not measurable, thus an observer is designed for each of the agents. Secondly, the methodology is extended to the leader–follower consensus control for a group of nonlinear mechanical systems. It is shown that the states of the mechanical systems can reach a consensus within finite time under input saturation. Finally, simulation results illustrate and verify the effectiveness of the proposed schemes.

[1]  Wenjie Dong,et al.  On consensus algorithms of multiple uncertain mechanical systems with a reference trajectory , 2011, Autom..

[2]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[3]  Wei Wang,et al.  Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots , 2014, Autom..

[4]  Xiaohua Xia,et al.  Adaptive consensus of multi-agents in networks with jointly connected topologies , 2012, Autom..

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

[6]  Yongduan Song,et al.  Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems , 2015, Autom..

[7]  Dongmei Xie,et al.  Consensus problem of data-sampled networked multi-agent systems with time-varying communication delays , 2013 .

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

[9]  Long Wang,et al.  Finite-time formation control for multi-agent systems , 2009, Autom..

[10]  Jie Huang,et al.  On an output feedback finite-time stabilization problem , 2001, IEEE Trans. Autom. Control..

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

[12]  Yanjiao Zhang,et al.  Finite-time consensus of second-order leader-following multi-agent systems without velocity measurements , 2013 .

[13]  Jie Huang,et al.  Finite-time control for robot manipulators , 2002, Syst. Control. Lett..

[14]  Yiguang Hong,et al.  Distributed Observers Design for Leader-Following Control of Multi-Agent Networks (Extended Version) , 2017, 1801.00258.

[15]  Jiangping Hu,et al.  Tracking control for multi-agent consensus with an active leader and variable topology , 2006, Autom..

[16]  Harry Septanto,et al.  Consensus-based controllers for spacecraft attitude alignment: Simulation results , 2011, 2011 2nd International Conference on Instrumentation, Communications, Information Technology, and Biomedical Engineering.

[17]  Khac Duc Do,et al.  Flocking for Multiple Elliptical Agents With Limited Communication Ranges , 2011, IEEE Transactions on Robotics.

[18]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[19]  Frank L. Lewis,et al.  Robot Manipulator Control: Theory and Practice , 2003 .

[20]  Hong Xia,et al.  Leader-following formation control for second-order multi-agent systems with time-varying delays , 2014 .

[21]  Jay A. Farrell,et al.  Decentralized cooperative control of multiple nonholonomic dynamic systems with uncertainty , 2009, Autom..

[22]  Shihua Li,et al.  Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics , 2011, Autom..

[23]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

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

[25]  Yongcan Cao,et al.  Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues , 2010 .

[26]  Przemyslaw Ignaciuk,et al.  Discrete-Time Sliding-Mode Congestion Control in Multisource Communication Networks With Time-Varying Delay , 2011, IEEE Transactions on Control Systems Technology.

[27]  Long Wang,et al.  Finite-Time Consensus Problems for Networks of Dynamic Agents , 2007, IEEE Transactions on Automatic Control.

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

[29]  J. Sheng,et al.  Leader-following consensus of a class of nonlinear multi-agent systems via dynamic output feedback control , 2015 .

[30]  Wenjie Dong,et al.  Adaptive consensus seeking of multiple nonlinear systems , 2012 .

[31]  Mehran Mesbahi,et al.  On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian , 2006, IEEE Transactions on Automatic Control.

[32]  Guanghui Wen,et al.  Distributed finite-time tracking control for multi-agent systems: An observer-based approach , 2013, Syst. Control. Lett..

[33]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[34]  L. Rosier.  Homogeneous Lyapunov function for homogeneous continuous vector field , 1992 .

[35]  George York,et al.  Cooperative Control of UAVs for Localization of Intermittently Emitting Mobile Targets , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[36]  K. D. Do,et al.  Formation Tracking Control of Unicycle-Type Mobile Robots With Limited Sensing Ranges , 2008, IEEE Transactions on Control Systems Technology.

[37]  Qian Ma,et al.  Consensus for nonlinear multi-agent systems with sampled data , 2014 .