Finite-Time Consensus of Stochastic Nonlinear Multi-agent Systems

This article studies the finite-time consensus of the stochastic nonlinear multi-agent systems under a directed communication topology. Since the inherent nonlinear dynamics and stochastic disturbances in multi-agent systems are completely unknown, the existing finite-time stability criterion becomes unavailable. To handle this difficulty, by applying the mean value theorem of integrals, a key finite-time stability criterion in integral form is first established. Then, based on the approximation property of the fuzzy logic systems, a distributed adaptive fuzzy control scheme is presented. Under the presented control strategy, the finite-time consensus of the stochastic nonlinear multi-agent systems is achieved. By applying Jessen’s inequality and Theorem  1 , the finite-time stability of the closed system is proved. Finally, the simulation result shows the validity of the distributed controller.

[1]  Mengyin Fu,et al.  Distributed containment control of multi‐agent systems with general linear dynamics in the presence of multiple leaders , 2013 .

[2]  Ligang Wu,et al.  Event-Triggered Fault Detection of Nonlinear Networked Systems , 2017, IEEE Transactions on Cybernetics.

[3]  Yongduan Song,et al.  Adaptive finite time coordinated consensus for high-order multi-agent systems: Adjustable fraction power feedback approach , 2016, Inf. Sci..

[4]  Guanrong Chen,et al.  Adaptive second-order consensus of networked mobile agents with nonlinear dynamics , 2011, Autom..

[5]  Jianmei Wang,et al.  Periodic solution and control optimization of a prey-predator model with two types of harvesting , 2018 .

[6]  Renquan Lu,et al.  Event-Triggered Consensus Control for Multi-Agent Systems Against False Data-Injection Attacks , 2019, IEEE Transactions on Cybernetics.

[7]  Hongyi Li,et al.  Event-Triggered Control for Multiagent Systems With Sensor Faults and Input Saturation , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[8]  Jianqiang Yi,et al.  Analysis and Design of Functionally Weighted Single-Input-Rule-Modules Connected Fuzzy Inference Systems , 2018, IEEE Transactions on Fuzzy Systems.

[9]  Frank L. Lewis,et al.  Cooperative adaptive control for synchronization of second‐order systems with unknown nonlinearities , 2011 .

[10]  Xiao Fan Wang,et al.  Rendezvous of multiple mobile agents with preserved network connectivity , 2010, Syst. Control. Lett..

[11]  C. L. Philip Chen,et al.  Fuzzy Adaptive Inverse Compensation Method to Tracking Control of Uncertain Nonlinear Systems With Generalized Actuator Dead Zone , 2017, IEEE Transactions on Fuzzy Systems.

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

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

[14]  Shaocheng Tong,et al.  Adaptive Neural Network Finite-Time Control for Multi-Input and Multi-Output Nonlinear Systems With Positive Powers of Odd Rational Numbers , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[15]  Hak-Keung Lam,et al.  Observer-Based Fault Detection for Nonlinear Systems With Sensor Fault and Limited Communication Capacity , 2016, IEEE Transactions on Automatic Control.

[16]  Wenshun Lv,et al.  Adaptive tracking control for a class of uncertain nonlinear systems with infinite number of actuator failures using neural networks , 2017, Advances in Difference Equations.

[17]  Xinzhu Meng,et al.  Geometrical analysis and control optimization of a predator-prey model with multi state-dependent impulse , 2017, Advances in Difference Equations.

[18]  Shaocheng Tong,et al.  Finite-Time Adaptive Fuzzy Output Feedback Dynamic Surface Control for MIMO Nonstrict Feedback Systems , 2019, IEEE Transactions on Fuzzy Systems.

[19]  Peter Xiaoping Liu,et al.  Adaptive Fuzzy Finite-Time Control of Nonlinear Systems With Actuator Faults , 2020, IEEE Transactions on Cybernetics.

[20]  Wei Lin,et al.  Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization , 2001 .

[21]  Yigang He,et al.  Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  Jianqiang Yi,et al.  Interval data driven construction of shadowed sets with application to linguistic word modelling , 2020, Inf. Sci..

[23]  Xuehua Li,et al.  Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems , 2017, IEEE Transactions on Cybernetics.

[24]  Xuan Cai,et al.  Consensus control of higher-order nonlinear multi-agent systems with unknown control directions , 2019, Neurocomputing.

[25]  Lin Zhao,et al.  Adaptive fuzzy control for induction motors stochastic nonlinear systems with input saturation based on command filtering , 2018, Inf. Sci..

[26]  Zhihong Man,et al.  Multi‐surface sliding control for fast finite‐time leader–follower consensus with high order SISO uncertain nonlinear agents , 2014 .

[27]  Yun Zhang,et al.  Observer-based finite time control of nonlinear systems with actuator failures , 2019, Inf. Sci..

[28]  Javad Askari,et al.  Distributed containment output-feedback control for a general class of stochastic nonlinear multi-agent systems , 2016, Neurocomputing.

[29]  Yun Zhang,et al.  Adaptive quantized fuzzy control of stochastic nonlinear systems with actuator dead-zone , 2016, Inf. Sci..

[30]  Renquan Lu,et al.  Finite-Horizon $H_{\infty}$ State Estimation for Periodic Neural Networks Over Fading Channels , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Lin Zhao,et al.  Barrier Lyapunov functions-based command filtered output feedback control for full-state constrained nonlinear systems , 2019, Autom..

[32]  Frank L. Lewis,et al.  Cooperative control with distributed gain adaptation and connectivity estimation for directed networks , 2014 .

[33]  Peter Xiaoping Liu,et al.  Adaptive Neural Output-Feedback Decentralized Control for Large-Scale Nonlinear Systems With Stochastic Disturbances , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[34]  Suiyang Khoo,et al.  Generalized Lyapunov criteria on finite-time stability of stochastic nonlinear systems , 2018, Autom..

[35]  Peng Shi,et al.  Finite-time command filtered backstepping control for a class of nonlinear systems , 2018, Autom..

[36]  C. L. Philip Chen,et al.  Adaptive Fuzzy Control for a Class of Stochastic Pure-Feedback Nonlinear Systems With Unknown Hysteresis , 2016, IEEE Transactions on Fuzzy Systems.

[37]  C. L. Philip Chen,et al.  Adaptive Quantized Controller Design Via Backstepping and Stochastic Small-Gain Approach , 2016, IEEE Transactions on Fuzzy Systems.

[38]  Bing Chen,et al.  Observer and Adaptive Fuzzy Control Design for Nonlinear Strict-Feedback Systems With Unknown Virtual Control Coefficients , 2018, IEEE Transactions on Fuzzy Systems.

[39]  Xiongxiong He,et al.  Robust adaptive consensus of nonstrict-feedback multi-agent systems with quantized input and unmodeled dynamics , 2019, Inf. Sci..

[40]  Yumei Sun,et al.  Finite-Time Fuzzy Control of Stochastic Nonlinear Systems , 2020, IEEE Transactions on Cybernetics.

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

[42]  Hongjing Liang,et al.  Neural-Based Decentralized Adaptive Finite-Time Control for Nonlinear Large-Scale Systems With Time-Varying Output Constraints , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[43]  Fang Wang,et al.  Adaptive Finite Time Control of Nonlinear Systems Under Time-Varying Actuator Failures , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[44]  Huaguang Zhang,et al.  Neural Observer and Adaptive Neural Control Design for a Class of Nonlinear Systems , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[45]  Feng Liu Boundedness and continuity of maximal operators associated to polynomial compound curves on Triebel-Lizorkin spaces , 2019, Mathematical Inequalities & Applications.

[46]  Yungang Liu,et al.  Finite-time consensus tracking for multi-agent systems with inherent uncertainties and disturbances , 2019, Int. J. Control.

[47]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control - design and stability analysis , 1994 .

[48]  Hongjing Liang,et al.  Adaptive Event-Triggered Fault Detection Scheme for Semi-Markovian Jump Systems With Output Quantization , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[49]  Zongli Lin,et al.  Global optimal consensus for higher-order multi-agent systems with bounded controls , 2019, Autom..

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

[51]  Bing Chen,et al.  Finite time control of switched stochastic nonlinear systems , 2019, Fuzzy Sets Syst..

[52]  Bing Chen,et al.  Distributed adaptive coordination control for uncertain nonlinear multi-agent systems with dead-zone input , 2016, J. Frankl. Inst..

[53]  Zhihong Man,et al.  Finite-time stability and instability of stochastic nonlinear systems , 2011, Autom..

[54]  Xuehua Li,et al.  Adaptive finite-time tracking control of switched nonlinear systems , 2017, Inf. Sci..

[55]  Xiaobo Li,et al.  Quantized consensus of second-order continuous-time multi-agent systems with a directed topology via sampled data , 2013, Autom..

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

[57]  C. L. Philip Chen,et al.  Adaptive finite-time control of stochastic nonlinear systems with actuator failures , 2019, Fuzzy Sets Syst..

[58]  Changchun Hua,et al.  Finite-time consensus tracking of second-order multi-agent systems via nonsingular TSM , 2014 .

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

[60]  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).

[61]  Yun Zhang,et al.  Event-Triggered Neural Control of Nonlinear Systems With Rate-Dependent Hysteresis Input Based on a New Filter , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[62]  Xiaoping Liu,et al.  Adaptive fuzzy asymptotical tracking control of nonlinear systems with unmodeled dynamics and quantized actuator , 2018, Inf. Sci..

[63]  Zhihong Man,et al.  Finite-time stabilization of stochastic nonlinear systems in strict-feedback form , 2013, Autom..

[64]  John T. Wen,et al.  Adaptive motion coordination: Using relative velocity feedback to track a reference velocity , 2009, Autom..

[65]  Zhihong Man,et al.  Finite-time stability theorems of homogeneous stochastic nonlinear systems , 2017, Syst. Control. Lett..

[66]  Jianmei Wang,et al.  Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy , 2018 .

[67]  Edward A. Patrick,et al.  Review of Pattern Recognition in Medical Diagnosis and Consulting Relative to a New System Model , 1974, IEEE Trans. Syst. Man Cybern..