Distributed adaptive leader-following tracking control of networked Lagrangian systems with unknown control directions under undirected/directed graphs

ABSTRACT This paper addresses the leader-following consensus problem of networked Lagrangian systems with unknown control directions and uncertain dynamics. For undirected graphs and directed graphs, two types of distributed control protocols are proposed without assuming that the leader's position information is linearly parameterised. It is proven that all signals in the closed-loop system are bounded, and a leader-following consensus can be achieved with the proposed corresponding protocols. These protocols are distributed in the sense that the control input for each Lagrangian system is solely based on local relative position and velocity information from its neighbourhood set and does not require additional information, e.g. acceleration or observer information of its neighbours, thus avoiding the dead-loop problem and reducing the communication burden. Simulations on networked two-link revolute joint arms are given to validate the theoretical findings.

[1]  Yongduan Song,et al.  Terminal Sliding Mode-Based Consensus Tracking Control for Networked Uncertain Mechanical Systems on Digraphs , 2018, IEEE Transactions on Neural Networks and Learning Systems.

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

[3]  Long Cheng,et al.  Adaptive neural network tracking control for manipulators with uncertain kinematics, dynamics and actuator model , 2009, Autom..

[4]  Chien Chern Cheah,et al.  Adaptive Jacobian tracking control of robots with uncertainties in kinematic, dynamic and actuator models , 2006, IEEE Transactions on Automatic Control.

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

[6]  Warren E. Dixon,et al.  Adaptive Regulation of Amplitude Limited Robot Manipulators With Uncertain Kinematics and Dynamics , 2007, IEEE Transactions on Automatic Control.

[7]  Baoli Ma,et al.  A new formation control of multiple underactuated surface vessels , 2018, Int. J. Control.

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

[9]  Guanghui Wen,et al.  Designing Fully Distributed Consensus Protocols for Linear Multi-Agent Systems With Directed Graphs , 2013, IEEE Transactions on Automatic Control.

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

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

[12]  Yun Zhang,et al.  Adaptive control of robotic systems with unknown actuator nonlinearities and control directions , 2015 .

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

[14]  Yun Zhang,et al.  Saturated Nussbaum Function Based Approach for Robotic Systems With Unknown Actuator Dynamics , 2016, IEEE Transactions on Cybernetics.

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

[16]  Z. Zuo,et al.  Adaptive trajectory tracking control of output constrained multi-rotors systems , 2014 .

[17]  Guangfu Ma,et al.  Distributed Coordinated Tracking With a Dynamic Leader for Multiple Euler-Lagrange Systems , 2011, IEEE Transactions on Automatic Control.

[18]  Long Cheng,et al.  Neural-Network-Based Adaptive Leader-Following Control for Multiagent Systems With Uncertainties , 2010, IEEE Transactions on Neural Networks.

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

[20]  Alexander Graham,et al.  Kronecker Products and Matrix Calculus: With Applications , 1981 .

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

[22]  Guangfu Ma,et al.  Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph , 2012, Autom..

[23]  Gang Wang,et al.  Distributed Leaderless and Leader-Following Consensus Control of Multiple Euler-Lagrange Systems with Unknown Control Directions , 2018, J. Intell. Robotic Syst..

[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]  Frank L. Lewis,et al.  Distributed Adaptive Tracking Control for Synchronization of Unknown Networked Lagrangian Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[26]  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.

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

[28]  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.

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

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

[31]  J. M. Peng,et al.  Robust cooperative output tracking of networked high-order power integrators systems , 2016, Int. J. Control.

[32]  Long Cheng,et al.  Decentralized adaptive consensus control for multi-manipulator system with uncertain dynamics , 2008, 2008 IEEE International Conference on Systems, Man and Cybernetics.