Leader-following consensus control of position-constrained multiple Euler-Lagrange systems with unknown control directions

Abstract This paper studies the distributed leader-following consensus control problems of position-constrained multiple Euler-Lagrange Systems (ELSs) with unknown control directions. The objective of our discussion is to develop a consensus protocol despite the existence of position constraints and unknown control directions in each agent. Most of the existing works related to state constraints are for single systems and rare results are concerned about multi-agent systems. With the help of the barrier Lyapunov function, Nussbaum gain adjusting technique, and adaptive control methodology, a novel leader-following consensus algorithm is successfully designed to make sure the convergence to zero of the consensus errors and the boundedness of the signals in the closed-loop system. Moreover, the position constraints for each agent are never violated for all time during the control process. The effectiveness of the main result is illustrated by a practical mechanical system.

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

[2]  Yurong Liu,et al.  A note on guaranteed cost control for nonlinear stochastic systems with input saturation and mixed time‐delays , 2017 .

[3]  Petter Ögren,et al.  Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment , 2004, IEEE Transactions on Automatic Control.

[4]  Wei Wang,et al.  Adaptive consensus control of output-constrained second-order nonlinear systems via neurodynamic optimization , 2017, Neurocomputing.

[5]  Gang Wang,et al.  Distributed consensus control for second-order nonlinear multi-agent systems with unknown control directions and position constraints , 2018, Neurocomputing.

[6]  Rafael Kelly,et al.  Control of Robot Manipulators in Joint Space , 2005 .

[7]  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.

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

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

[10]  Zidong Wang,et al.  On Kalman-Consensus Filtering With Random Link Failures Over Sensor Networks , 2018, IEEE Transactions on Automatic Control.

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

[12]  Shaocheng Tong,et al.  Barrier Lyapunov Functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints , 2016, Autom..

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

[14]  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.

[15]  Keng Peng Tee,et al.  Control of nonlinear systems with time-varying output constraints , 2009, 2009 IEEE International Conference on Control and Automation.

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

[17]  Donghua Zhou,et al.  Event-Based $H_{\infty}$ Consensus Control of Multi-Agent Systems With Relative Output Feedback: The Finite-Horizon Case , 2015, IEEE Transactions on Automatic Control.

[18]  Gang Wang,et al.  Distributed adaptive leader-following tracking control of networked Lagrangian systems with unknown control directions under undirected/directed graphs , 2019, Int. J. Control.

[19]  Shaocheng Tong,et al.  Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems , 2017, Autom..

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

[21]  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.

[22]  Yuming Bo,et al.  Quasi-Consensus Control for a Class of Time-Varying Stochastic Nonlinear Time-Delay Multiagent Systems Subject to Deception Attacks , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

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

[24]  Randal W. Beard,et al.  Multiple UAV Coalitions for a Search and Prosecute Mission , 2011, J. Intell. Robotic Syst..

[25]  Xu Jin,et al.  Adaptive Fixed-Time Control for MIMO Nonlinear Systems With Asymmetric Output Constraints Using Universal Barrier Functions , 2019, IEEE Transactions on Automatic Control.

[26]  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.

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

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

[29]  Yongduan Song,et al.  Prescribed Performance Control of Uncertain Euler–Lagrange Systems Subject to Full-State Constraints , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[30]  R. Nussbaum.  Some remarks on a conjecture in parameter adaptive control , 1983 .

[31]  Petros G. Voulgaris,et al.  Distributed Coordination Control for Multi-Robot Networks Using Lyapunov-Like Barrier Functions , 2016, IEEE Transactions on Automatic Control.

[32]  Yurong Liu,et al.  Distributed filtering for nonlinear time‐delay systems over sensor networks subject to multiplicative link noises and switching topology , 2019, International Journal of Robust and Nonlinear Control.

[33]  Francis Eng Hock Tay,et al.  Barrier Lyapunov Functions for the control of output-constrained nonlinear systems , 2009, Autom..

[34]  Keng Peng Tee,et al.  Control of nonlinear systems with partial state constraints using a barrier Lyapunov function , 2011, Int. J. Control.

[35]  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.

[36]  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).

[37]  Hongjing Liang,et al.  Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints , 2018, Appl. Math. Comput..

[38]  Xudong Ye,et al.  Cooperative control of high-order nonlinear systems with unknown control directions , 2018, Syst. Control. Lett..

[39]  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.

[40]  Yongduan Song,et al.  Removing the Feasibility Conditions Imposed on Tracking Control Designs for State-Constrained Strict-Feedback Systems , 2019, IEEE Transactions on Automatic Control.

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