Decentralized Control of Networked Systems with Unknown Control Directions and Uncertainties

In this paper, we investigate the decentralized control of networked agents with unknown control directions, i.e., the sign of high-frequency-gain in agent’s dynamics is unknown. Meanwhile, uncertain nonlinearity also appears in agent’s dynamics. A Nussbaum-type adaptive controller is designed with the aid of nonlinear damping technique for each agent such that consensus of the network can be achieved while all signals in the overall system maintain bounded. The controller for each agent is composed by a Nussbaum-type item which seeks the control direction adaptively and a distributed item to drive the system to consensus state, in which a nonlinear damping item is added. It is proved that consensus of the network can be realized via the proposed controller. Moreover, the final consensus state is indicated, which is significant for consensus of networked nonlinear systems. Simulation results are presented to verify the effectiveness of the proposed controllers.

[1]  Xudong Ye,et al.  Decentralized Adaptive Stabilization of Large-Scale Nonlinear Time-Delay Systems With Unknown High-Frequency-Gain Signs , 2011, IEEE Transactions on Automatic Control.

[2]  Zheng Wang,et al.  Adaptive output consensus tracking of uncertain multi-agent systems , 2011, Proceedings of the 2011 American Control Conference.

[3]  Haibo Ji,et al.  Robust consensus tracking for a class of heterogeneous second‐order nonlinear multi‐agent systems , 2015 .

[4]  Jinde Cao,et al.  Distributed node-to-node consensus of multi-agent systems with time-varying pinning links , 2015, Neurocomputing.

[5]  Peng-Yung Woo,et al.  Iterative learning control for manipulator trajectory tracking without any control singularity , 2002, Robotica.

[6]  Sandip Roy,et al.  Constructing consensus controllers for networks with identical general linear agents , 2010 .

[7]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[8]  Rodolphe Sepulchre,et al.  Synchronization in networks of identical linear systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[9]  Tianyou Chai,et al.  Online Solution of Two-Player Zero-Sum Games for Continuous-Time Nonlinear Systems With Completely Unknown Dynamics , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Hyungbo Shim,et al.  Output Consensus of Heterogeneous Uncertain Linear Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[11]  X. Ye,et al.  Adaptive nonlinear design without a priori knowledge of control directions , 1998, IEEE Trans. Autom. Control..

[12]  Jie Huang,et al.  Stability of a Class of Linear Switching Systems with Applications to Two Consensus Problems , 2011, IEEE Transactions on Automatic Control.

[13]  C. L. Philip Chen,et al.  Fuzzy Observed-Based Adaptive Consensus Tracking Control for Second-Order Multiagent Systems With Heterogeneous Nonlinear Dynamics , 2016, IEEE Transactions on Fuzzy Systems.

[14]  Xin-Ping Guan,et al.  Leader-Following Output Consensus for High-Order Nonlinear Multiagent Systems , 2019, IEEE Transactions on Automatic Control.

[15]  Bikash C. Pal,et al.  Decentralized Nonlinear Control for Power Systems Using Normal Forms and Detailed Models , 2018, IEEE Transactions on Power Systems.

[16]  Xudong Ye,et al.  Decentralized adaptive regulation with unknown high-frequency-gain signs , 1999, IEEE Trans. Autom. Control..

[17]  Ali Saberi,et al.  Output synchronization for heterogeneous networks of non-introspective agents , 2012, Autom..

[18]  Lihua Xie,et al.  Network Topology and Communication Data Rate for Consensusability of Discrete-Time Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[19]  Guoqiang Hu,et al.  Robust finite-time connectivity preserving consensus tracking and formation control for multi-agent systems , 2017, 2017 American Control Conference (ACC).

[20]  Lin Huang,et al.  Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[21]  Ahmed Rahmani,et al.  Distributed finite-time consensus tracking for nonlinear multi-agent systems with a time-varying reference state , 2016, Int. J. Syst. Sci..

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

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

[24]  Maria Domenica Di Benedetto,et al.  Decentralized Supervisory Control of Networks of Nonlinear Control Systems , 2016, IEEE Transactions on Automatic Control.

[25]  Xudong Ye,et al.  Distributed adaptive controller for the output-synchronization of networked systems in semi-strict feedback form , 2014, J. Frankl. Inst..

[26]  Rodolphe Sepulchre,et al.  Synchronization in networks of identical linear systems , 2009, Autom..

[27]  Wei Wang,et al.  Adaptive consensus tracking control of uncertain nonlinear systems: A first-order example , 2012, 2012 12th International Conference on Control Automation Robotics & Vision (ICARCV).

[28]  Qi Zhou,et al.  Observer-Based Event-Triggered Adaptive Decentralized Fuzzy Control for Nonlinear Large-Scale Systems , 2019, IEEE Transactions on Fuzzy Systems.

[29]  Frank Allgöwer,et al.  An internal model principle is necessary and sufficient for linear output synchronization , 2011, Autom..

[30]  Sezai Emre Tuna,et al.  Conditions for Synchronizability in Arrays of Coupled Linear Systems , 2008, IEEE Transactions on Automatic Control.

[31]  Weihua Gui,et al.  Distributed Containment Control of Continuous-Time Multiagent Systems With Nonconvex Control Input Constraints , 2019, IEEE Transactions on Industrial Electronics.

[32]  X. Ye,et al.  Decentralised adaptive control for large-scale non-linear systems with unknown high-frequency-gain signs , 2005 .

[33]  Wei Ren,et al.  Multi-vehicle consensus with a time-varying reference state , 2007, Syst. Control. Lett..

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

[35]  Frank L. Lewis,et al.  Lyapunov, Adaptive, and Optimal Design Techniques for Cooperative Systems on Directed Communication Graphs , 2012, IEEE Transactions on Industrial Electronics.

[36]  Andrew G. Alleyne,et al.  Nonlinear adaptive control of active suspensions , 1995, IEEE Trans. Control. Syst. Technol..

[37]  Zhenhua Wang,et al.  Consensus problems in networks of agents with communication delay , 2015, 2015 IEEE Conference on Control Applications (CCA).

[38]  Xinping Guan,et al.  Leader-Following Consensus for High-Order Nonlinear Stochastic Multiagent Systems , 2017, IEEE Transactions on Cybernetics.

[39]  A. Morse,et al.  Adaptive stabilization of linear systems with unknown high-frequency gains , 1984, The 23rd IEEE Conference on Decision and Control.

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

[41]  Jan Lunze,et al.  Synchronization of Heterogeneous Agents , 2012, IEEE Transactions on Automatic Control.

[42]  Zhong-Ping Jiang,et al.  A unifying framework for global regulation via nonlinear output feedback: from ISS to iISS , 2004, IEEE Transactions on Automatic Control.

[43]  Zhong-Ping Jiang,et al.  Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties , 1998, Autom..

[44]  Xinghu Wang,et al.  Consensus control of nonlinear leader-follower multi-agent systems with actuating disturbances , 2014, Syst. Control. Lett..