scholarly journals Pinning-Like Adaptive Consensus for Networked Mobile Agents with Heterogeneous Nonlinear Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Chengjie Xu ◽  
Yanwei Wang ◽  
Hong Zhang ◽  
Xiaoqi Zhou
Keyword(s):  
Nonlinear Dynamics ◽  
Adaptive Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Mobile Agents ◽  
Pinning Control ◽  
Adaptive Strategy ◽  
Global Information ◽  
First Order ◽  
Coupling Strengths

This paper investigates the adaptive consensus for networked mobile agents with heterogeneous nonlinear dynamics. Using tools from matrix, graph, and Lyapunov stability theories, sufficient consensus conditions are obtained under adaptive control protocols for both first-order and second-order cases. We design an adaptive strategy on the coupling strengths, which can guarantee that the consensus conditions do not require any global information except a connection assumption. The obtained results are also extended to networked mobile agents with identical nonlinear dynamics via adaptive pinning control. Finally, numerical simulations are presented to illustrate the theoretical findings.

scholarly journals Adaptive Synchronization of Complex Dynamical Networks with State Predictor

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yuntao Shi ◽  
Bo Liu ◽  
Xiao Han
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulations ◽  
Lyapunov Method ◽  
Adaptive Strategy ◽  
Convergence Speed ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Dynamical Networks ◽  
Synchronous State ◽  
Coupling Strengths

This paper addresses the adaptive synchronization of complex dynamical networks with nonlinear dynamics. Based on the Lyapunov method, it is shown that the network can synchronize to the synchronous state by introducing local adaptive strategy to the coupling strengths. Moreover, it is also proved that the convergence speed of complex dynamical networks can be increased via designing a state predictor. Finally, some numerical simulations are worked out to illustrate the analytical results.

scholarly journals Pinning synchronization of the drive and response dynamical networks with lag

2014 ◽  
Vol 24 (3) ◽  
pp. 257-270 ◽  
Author(s):  
Bohui Wen ◽  
Mo Zhao ◽  
Fanyu Meng
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Schur Complement ◽  
Pinning Control ◽  
Lag Synchronization ◽  
Dynamical Networks ◽  
General Complex ◽  
Minimum Number

Abstract This paper investigates the pinning synchronization of two general complex dynamical networks with lag. The coupling configuration matrices in the two networks are not need to be symmetric or irreducible. Several convenient and useful criteria for lag synchronization are obtained based on the lemma of Schur complement and the Lyapunov stability theory. Especially, the minimum number of controllers in pinning control can be easily obtained. At last, numerical simulations are provided to verify the effectiveness of the criteria

Dual Combination Synchronization of Six Chaotic Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Junwei Sun ◽  
Suxia Jiang ◽  
Guangzhao Cui ◽  
Yanfeng Wang
Keyword(s):  
Adaptive Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Combination Synchronization

Based on combination synchronization of three chaotic systems and combination–combination synchronization of four chaotic systems, a novel scheme of dual combination synchronization is investigated for six chaotic systems in the paper. Using combined adaptive control and Lyapunov stability theory of chaotic systems, some sufficient conditions are attained to realize dual combination synchronization of six chaotic systems. The corresponding theoretical proofs and numerical simulations are presented to demonstrate the effectiveness and correctness of the dual combination synchronization. Due to the complexity of dual combination synchronization, it will be more secure and interesting to transmit and receive signals in application of communication.

scholarly journals Consensus Tracking for Multiagent Systems with Nonlinear Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Runsha Dong
Keyword(s):  
Nonlinear Dynamics ◽  
Nonlinear Systems ◽  
Numerical Simulations ◽  
Multiagent Systems ◽  
Second Order ◽  
Control Laws ◽  
First Order ◽  
Consensus Tracking ◽  
Network Topologies ◽  
Theoretical Results

This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to verify the theoretical results.

scholarly journals Cluster Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control

2011 ◽  
Vol 2011 ◽  
pp. 1-23 ◽  
Author(s):  
Jianwen Feng ◽  
Jingyi Wang ◽  
Chen Xu ◽  
Francis Austin
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Topological Structure ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
General Complex ◽  
Coupling Strengths ◽  
Theoretical Results

We consider a method for driving general complex networks into prescribed cluster synchronization patterns by using pinning control. The coupling between the vertices of the network is nonlinear, and sufficient conditions are derived analytically for the attainment of cluster synchronization. We also propose an effective way of adapting the coupling strengths of complex networks. In addition, the critical combination of the control strength, the number of pinned nodes and coupling strength in each cluster are given by detailed analysis cluster synchronization of a special topological structure complex network. Our theoretical results are illustrated by numerical simulations.

Fixed-time tracking control for two-link rigid manipulator based on disturbance observer

2021 ◽  
pp. 014233122098363
Author(s):  
Heli Gao ◽  
Mou Chen
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Tracking Control ◽  
Disturbance Observer ◽  
Inverse Dynamics ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Extended State

This paper studies the fixed-time disturbance estimate and tracking control for two-link manipulators subjected to external disturbance. A fixed-time extended-state disturbance observer (FxTESDO) is proposed by improving the extended state observer. Also, a fixed-time inverse dynamics tracking control (FxTIDTC) scheme based on the FxTESDO is given for two-link manipulators. The fixed-time convergence of the FxTESDO and FxTIDTC is proved by the Lyapunov stability theory and with the aid of the bi-limit homogeneous technique. Numerical simulations are employed to illustrate the effectiveness of the proposed FxTIDTC.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

Dynamics of a Supported Cylinder in Axial Flow

2011 ◽  
Vol 99-100 ◽  
pp. 1059-1062
Author(s):  
Ji Duo Jin ◽  
Ning Li ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Analysis ◽  
Numerical Simulations ◽  
Nonlinear Model ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Viscous Force ◽  
Friction Drag ◽  
Flutter Instability ◽  
Nonlinear Force

The nonlinear dynamics are studied for a supported cylinder subjected to axial flow. A nonlinear model is presented for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are the quadratic viscous force and the structural nonlinear force induced by the lateral motions of the cylinder. Using two-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain the flutter instability found in the experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. The effect of the friction drag coefficients on the behavior of the system is investigated.

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