scholarly journals Observer-Type Consensus Protocol for a Class of Fractional-Order Uncertain Multiagent Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Hongjie Li
Keyword(s):  
Multiagent Systems ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Order System ◽  
Linear Matrix ◽  
Consensus Protocol ◽  
Stabilizing Controllers ◽  
Linear Matrix Inequality Approach ◽  
Value Decomposition ◽  
Theoretical Results

This paper investigates the consensus problem for a class of fractional-order uncertain multiagent systems with general linear node dynamics. Firstly, an observer-type consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on property of the Kronecker product and stability theory of fractional-order system, some sufficient conditions are presented for robust asymptotical stability of the observer-based fractional-order control systems. Thirdly, robust stabilizing controllers are derived by using linear matrix inequality approach and matrix’s singular value decomposition. Our results are in the form of linear matrix inequalities which can easily be solved by LMI toolbox in MATLAB. Finally, a numerical simulation is performed to show the effectiveness of the theoretical results.

scholarly journals H∞Consensus for Multiagent Systems with Heterogeneous Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Beibei Wang ◽  
Yuangong Sun
Keyword(s):  
Multiagent Systems ◽  
Multiagent System ◽  
Sufficient Conditions ◽  
Order System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Reduced Order ◽  
Heterogeneous Delays ◽  
Theoretical Results

We apply the linear matrix inequality method to consensus andH∞consensus problems of the single integrator multiagent system with heterogeneous delays in directed networks. To overcome the difficulty caused by heterogeneous time-varying delays, we rewrite the multiagent system into a partially reduced-order system and an integral system. As a result, a particular Lyapunov function is constructed to derive sufficient conditions for consensus of multiagent systems with fixed (switched) topologies. We also apply this method to theH∞consensus of multiagent systems with disturbances and heterogeneous delays. Numerical examples are given to illustrate the theoretical results.

scholarly journals Adaptive Guaranteed-Performance Consensus Control for Multi-Agent Systems with an Adjustable Convergence Speed

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Haiying Ma ◽  
Xiao Jia ◽  
Ning Cai ◽  
Jianxiang Xi
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Convergence Speed ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Consensus Control ◽  
Control Gain ◽  
Multi Agent ◽  
The Stability ◽  
Theoretical Results

In this paper, adaptive guaranteed-performance consensus control problems for multiagent systems with an adjustable convergence speed are investigated. A novel adaptive guaranteed-performance consensus protocol is proposed, where the communication weights can be adaptively regulated. By the state space decomposition method and the stability theory, sufficient conditions for guaranteed-performance consensus are obtained and the guaranteed-performance cost is determined. Moreover, the lower bound of the convergence coefficient for multiagent systems is deduced, which is linearly adjustable approximately by changing the adaptive control gain. Finally, simulation examples are introduced to demonstrate theoretical results.

scholarly journals Bipartite Consensus of Heterogeneous Multiagent Systems Based on Distributed Event-Triggered Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoyu Wang ◽  
Kaien Liu ◽  
Zhijian Ji ◽  
Shitao Han
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Input Delay ◽  
Consensus Problem ◽  
Consensus Protocol ◽  
Control Scheme ◽  
Event Triggering ◽  
Bipartite Consensus ◽  
Theoretical Results ◽  
Event Triggered

In this paper, the bipartite consensus problem of heterogeneous multiagent systems composed of first-order and second-order agents is considered by utilizing the event-triggered control scheme. Under structurally balanced directed topology, event-triggered bipartite consensus protocol is put forward, and event-triggering functions consisting of measurement error and threshold are designed. To exclude Zeno behavior, an exponential function is introduced in the threshold. The bipartite consensus problem is transformed into the corresponding stability problem by means of gauge transformation and model transformation. By virtue of Lyapunov method, sufficient conditions for systems without input delay are obtained to guarantee bipartite consensus. Furthermore, for the case with input delay, sufficient conditions which include an admissible upper bound of the delay are obtained to guarantee bipartite consensus. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

scholarly journals Consensus Conditions for a Class of Fractional-Order Nonlinear Multiagent Systems with Constant and Time-Varying Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiaorong Zhang ◽  
Min Shi
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Constant Time Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay ◽  
Theoretical Results

The consensus problem for a class of fractional-order nonlinear multiagent systems with a distributed protocol containing input time delay is investigated in this paper. Consider both cases of constant time delay and time-varying delay, the delay-independent consensus conditions are obtained to achieve the consensus of the systems, respectively, by adopting the linear matrix inequality (LMI) methods and stability theory of fractional-order systems. As illustrated by the numerical examples, the proposed theoretical results work well and accurately.

scholarly journals Group Consensus of Heterogeneous Multiagent Systems with Time Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Weixun Li ◽  
Liqiong Zhang
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Control Algorithm ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Group Consensus ◽  
Communication Time ◽  
Theoretical Results

In this paper, a neighbour-based control algorithm of group consensus is designed for a class of hybrid-based heterogeneous multiagent systems with communication time delay. We consider the statics leaders and active leaders, respectively. The original systems are transformed into new error systems by transformation. On the basis of the systems, applying Lyapunov stability theory and adopting the linear matrix inequality method, sufficient conditions which guarantee the heterogeneous multiagent systems stability are obtained. To illustrate the validity of theoretical results, some numerical simulations are given at the end of the paper.

scholarly journals Collaboration Control of Fractional-Order Multiagent Systems with Sampling Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hong-yong Yang ◽  
Lei Guo ◽  
Banghai Xu ◽  
Jian-zhong Gu
Keyword(s):  
Multiagent Systems ◽  
Fractional Order ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Sampled Data ◽  
Derivative Operator ◽  
Collaborative Control ◽  
Data Control ◽  
Theoretical Results

Because of the complexity of the practical environments, many distributed multiagent systems cannot be illustrated with the integer-order dynamics and can only be described with the fractional-order dynamics. In this paper, collaboration control problems of continuous-time networked fractional-order multiagent systems via sampled control and sampling delay are investigated. Firstly, the sampled-data control of multiagent systems with fractional-order derivative operator is analyzed in a directed weighted network ignoring sampling delay. Then, the collaborative control of fractional-order multiagent systems with sampled data and sampling delay is studied in a directed and symmetrical network. Many sufficient conditions for reaching consensus with sampled data and sampling delay are obtained. Some numerical simulations are presented to illustrate the utility of our theoretical results.

scholarly journals Performance Index Based Observer-Type Iterative Learning Control for Consensus Tracking of Uncertain Nonlinear Fractional-Order Multiagent Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Liming Wang ◽  
Guoshan Zhang
Keyword(s):  
Dimensional Analysis ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Performance Index ◽  
Sufficient Conditions ◽  
Iterative Learning ◽  
Linear Matrix ◽  
Two Dimensional ◽  
System Matrix ◽  
Monotonic Convergence

This paper is devoted to the perfect tracking problem of consensus and the monotonic convergence problem of input errors for the uncertain nonlinear fractional-order multiagent systems (FOMASs), where there exist the linear coupling relations between the fractional order, the perturbations of the system matrix, and input matrix. For the FOMASs including one leader agent and multiple follower agents, an observer-type fractional-order iterative learning consensus protocol is proposed. Based on the two-dimensional analysis for the FOMASs, a novel performance index, which can exhibit the monotonic convergence of the input errors, is constructed by using the definition of fractional integral. A Lyapunov-like method is applied to derive the sufficient conditions in terms of linear matrix inequalities, which can guarantee the perfect tracking of consensus and the monotonic convergence of input errors. Finally, the numerical simulation results including comparisons to traditional two-dimensional analysis are presented to demonstrate the effectiveness of the proposed methods.

scholarly journals Synchronization of Fractional Order Uncertain BAM Competitive Neural Networks

2021 ◽  
Vol 6 (1) ◽  
pp. 14
Author(s):  
M. Syed Ali ◽  
M. Hymavathi ◽  
Syeda Asma Kauser ◽  
Grienggrai Rajchakit ◽  
Porpattama Hammachukiattikul ◽  
...  
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Bidirectional Associative Memory ◽  
Numerical Examples ◽  
Novel Approach ◽  
Theoretical Results

This article examines the drive-response synchronization of a class of fractional order uncertain BAM (Bidirectional Associative Memory) competitive neural networks. By using the differential inclusions theory, and constructing a proper Lyapunov-Krasovskii functional, novel sufficient conditions are obtained to achieve global asymptotic stability of fractional order uncertain BAM competitive neural networks. This novel approach is based on the linear matrix inequality (LMI) technique and the derived conditions are easy to verify via the LMI toolbox. Moreover, numerical examples are presented to show the feasibility and effectiveness of the theoretical results.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

Guaranteed cost and finite-time event-triggered control of fractional-order switched systems

2021 ◽  
pp. 014233122110048
Author(s):  
Yilin Shang ◽  
Leipo Liu ◽  
Yifan Di ◽  
Zhumu Fu ◽  
Bo Fan
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Electrical Circuit ◽  
Linear Matrix ◽  
Current State ◽  
Guaranteed Cost ◽  
Event Triggered

This paper considers the problem of guaranteed cost and finite-time event-triggered control of fractional-order switched systems. Firstly, an event-triggered scheme including both the information of current state and an exponential decay function is proposed, and a novel cost function that adopts the characteristics of fractional-order integration is presented. Secondly, some sufficient conditions are derived to guarantee that the corresponding closed-loop system is finite-time stable with a certain cost upper bound, using multiple Lyapunov functions and average dwell time approach. Meanwhile, the event-triggered parameters and state feedback gains are simultaneously obtained via solving linear matrix inequalities. Moreover, Zeno behavior does not exist by finding a positive lower bound of the triggered interval. Finally, an example about fractional-order switched electrical circuit is provided to show the effectiveness of the proposed method.

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