Consensus control of higher-order nonlinear multi-agent systems with unknown control directions

Abstract In this paper, we investigate the distributed consensus control of higher-order nonlinear multi-agent systems under directed graphs. We consider two cases: (i) multi-agents with unknown identical control directions and uncertain dynamics, and (ii) multi-agents with unknown nonidentical control directions and known dynamics. In the first case, a distributed adaptive control protocol is designed based on neural networks (NN) and Nussbaum functions. In the second case, a distributed nonlinear PI control protocol is proposed. It is proved via Lyapunov stability analysis that our developed protocols can ensure the asymptotical convergence of the consensus errors and global uniform boundedness of all the closed-loop signals. Theoretical results are verified by numerical simulations.

[1]  Youfeng Su,et al.  Cooperative Global Output Regulation of Second-Order Nonlinear Multi-Agent Systems With Unknown Control Direction , 2015, IEEE Transactions on Automatic Control.

[2]  Long Cheng,et al.  Decentralized Robust Adaptive Control for the Multiagent System Consensus Problem Using Neural Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  Wei Ren,et al.  Distributed leaderless consensus algorithms for networked Euler–Lagrange systems , 2009, Int. J. Control.

[4]  Xudong Ye,et al.  Cooperative control of multiple heterogeneous agents with unknown high-frequency-gain signs , 2014, Syst. Control. Lett..

[5]  Tao Zhang,et al.  Stable Adaptive Neural Network Control , 2001, The Springer International Series on Asian Studies in Computer and Information Science.

[6]  Frank L. Lewis,et al.  Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics , 2012, Autom..

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

[8]  Alessandro Astolfi,et al.  Two solutions to the adaptive visual servoing problem , 2001, IEEE Trans. Robotics Autom..

[9]  Zongli Lin,et al.  Distributed Consensus Control of Multi-Agent Systems With Higher Order Agent Dynamics and Dynamically Changing Directed Interaction Topologies , 2016, IEEE Transactions on Automatic Control.

[10]  M. Spong,et al.  Robot Modeling and Control , 2005 .

[11]  C. L. Philip Chen,et al.  Adaptive Consensus of Nonlinear Multi-Agent Systems With Non-Identical Partially Unknown Control Directions and Bounded Modelling Errors , 2017, IEEE Transactions on Automatic Control.

[12]  Wei Wang,et al.  Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances , 2017, Autom..

[13]  Wenjie Dong,et al.  Flocking of Multiple Mobile Robots Based on Backstepping , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  Gang Wang,et al.  Designing distributed consensus protocols for second-order nonlinear multi-agents with unknown control directions under directed graphs , 2017, J. Frankl. Inst..

[15]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[16]  Gang Wang,et al.  Distributed adaptive consensus tracking control of higher-order nonlinear strict-feedback multi-agent systems using neural networks , 2016, Neurocomputing.

[17]  Jie Chen,et al.  Distributed Consensus of Second-Order Multi-Agent Systems With Heterogeneous Unknown Inertias and Control Gains Under a Directed Graph , 2016, IEEE Transactions on Automatic Control.

[18]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[19]  Frank L. Lewis,et al.  Cooperative Globally Optimal Control for Multi-Agent Systems on Directed Graph Topologies , 2014 .

[20]  Frank L. Lewis,et al.  Neural Network Control Of Robot Manipulators And Non-Linear Systems , 1998 .

[21]  Hongwei Zhang,et al.  Cooperative output feedback adaptive control of uncertain nonlinear multi-agent systems with a dynamic leader , 2015, Neurocomputing.

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

[23]  Gang Wang,et al.  Distributed adaptive output consensus tracking of higher-order systems with unknown control directions , 2016, Neurocomputing.

[24]  Haris E. Psillakis,et al.  Consensus in Networks of Agents With Unknown High-Frequency Gain Signs and Switching Topology , 2017, IEEE Transactions on Automatic Control.

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

[26]  Yongsheng Zhao,et al.  Adaptive Autopilot Design of Time-Varying Uncertain Ships With Completely Unknown Control Coefficient , 2007, IEEE Journal of Oceanic Engineering.

[27]  Xiaobo Li,et al.  Adaptive Consensus of Multi-Agent Systems With Unknown Identical Control Directions Based on A Novel Nussbaum-Type Function , 2014, IEEE Transactions on Automatic Control.