Consensus Tracking of Fractional-Order Multiagent Systems via Fractional-Order Iterative Learning Control

In this work, the consensus problem of fractional-order multiagent systems with the general linear model of fixed topology is studied. Both distributed PDα-type and Dα-type fractional-order iterative learning control (FOILC) algorithms are proposed. Here, a virtual leader is introduced to generate the desired trajectory, fixed communication topology is considered, and only a subset of followers can access the desired trajectory. The convergence conditions are proved using graph theory, fractional calculus, and λ norm theory. The theoretical analysis shows that the output of each agent completely tracks the expected trajectory in a limited time as the iteration number increases for both PDα-type and Dα-type FOILC algorithms. Extensive numerical simulations are given to demonstrate the feasibility and effectiveness.

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Fractional-Order Iterative Learning Control with Initial State Learning for a Class of Multiagent Systems

Complexity ◽

10.1155/2020/9130875 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14

Author(s):

Xungen Li ◽

Shuaishuai Lv ◽

Mian Pan ◽

Qi Ma ◽

Wenyu Cai

Keyword(s):

Multiagent Systems ◽

Fractional Order ◽

Iterative Learning Control ◽

Closed Loop ◽

Learning Control ◽

Iterative Learning ◽

Initial State ◽

Convergence Conditions ◽

Fractional Order Calculus ◽

State Learning

To solve the consensus problem of fractional-order multiagent systems with nonzero initial states, both open- and closed-loop PDα-type fractional-order iterative learning control are presented. Considering the nonzero states, an initial state learning mechanism is designed. The finite time convergences of the proposed methods are discussed in detail and strictly proved by using Lebesgue-p norm theory and fractional-order calculus. The convergence conditions of the proposed algorithms are presented. Finally, some simulations are applied to verify the effectiveness of the proposed methods.

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Consensus Learning Control for Leader-Following Nonlinear Multiagent Systems with Control Delay

Wireless Communications and Mobile Computing ◽

10.1155/2019/2035683 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10

Author(s):

Xiongfeng Deng ◽

Xiuxia Sun ◽

Shuguang Liu

Keyword(s):

Time Delay ◽

Multiagent Systems ◽

Iterative Learning Control ◽

Learning Control ◽

Control Delay ◽

Consensus Tracking ◽

Control Scheme ◽

Communication Topology ◽

Leader Following ◽

Theoretical Results

In this paper, the consensus tracking problem of leader-following nonlinear control time-delay multiagent systems with directed communication topology is addressed. An improved high-order iterative learning control scheme with time-delay is proposed, where the local information between agents is considered. The uniformly global Lipschitz condition is applied to deal with the nonlinear dynamics. Then, a sufficient condition is driven, which guarantees that all the following agents track the trajectory of leader. Also, the convergence of proposed control protocol is analyzed by the norm theory. Finally, two cases are provided to illustrate the validity of theoretical results.

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Formation Tracking via Iterative Learning Control for Multiagent Systems with Diverse Communication Time-Delays

Mathematical Problems in Engineering ◽

10.1155/2019/8164297 ◽

2019 ◽

Vol 2019 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Jialu Zhang ◽

Yong Fang ◽

Chenlong Li ◽

Wenbo Zhu

Keyword(s):

Multiagent Systems ◽

Iterative Learning Control ◽

Time Delays ◽

Learning Control ◽

Frequency Domain Analysis ◽

Iterative Learning ◽

Convergence Conditions ◽

Formation Tracking ◽

Communication Time ◽

Nyquist Stability

In this paper, we consider the formation tracking problem for multiagent systems with diverse communication time-delays by using iterative learning control (ILC) method based on the frequency domain analysis. A first-order ILC law for multiagent systems with diverse communication time-delays is first proposed and its convergence conditions are given by the general Nyquist stability criterion and Gershgorin’s disk theorem. Then, in order for the system to track accurately, a second-order ILC law is presented. The conditions for system tracking with zero error are established. Numerical simulations show that the proposed ILC laws for multiagent systems with diverse communication time-delays are able to achieve effectively formation tracking. And the convergence speed remains the same as the learning control algorithm without communication delay.

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Consensus Tracking by Iterative Learning Control for Linear Heterogeneous Multiagent Systems Based on Fractional-Power Error Signals

Algorithms ◽

10.3390/a12090185 ◽

2019 ◽

Vol 12 (9) ◽

pp. 185 ◽

Cited By ~ 1

Author(s):

Yu-Juan Luo ◽

Cheng-Lin Liu ◽

Guang-Ye Liu

Keyword(s):

Multiagent Systems ◽

Iterative Learning Control ◽

Tracking Error ◽

Fractional Power ◽

Learning Control ◽

Convergence Condition ◽

Iterative Learning ◽

Reference Trajectory ◽

Order Tracking ◽

Consensus Tracking

This paper deals with the consensus tracking problem of heterogeneous linear multiagent systems under the repeatable operation environment, and adopts a proportional differential (PD)-type iterative learning control (ILC) algorithm based on the fractional-power tracking error. According to graph theory and operator theory, convergence condition is obtained for the systems under the interconnection topology that contains a spanning tree rooted at the reference trajectory named as the leader. Our algorithm based on fractional-power tracking error achieves a faster convergence rate than the usual PD-type ILC algorithm based on the integer-order tracking error. Simulation examples illustrate the correctness of our proposed algorithm.

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Iterative Learning Consensus Control for Nonlinear Partial Difference Multiagent Systems with Time Delay

Complexity ◽

10.1155/2021/8886945 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Cun Wang ◽

Xisheng Dai ◽

Kene Li ◽

Zupeng Zhou

Keyword(s):

Time Delay ◽

Multiagent Systems ◽

Learning Algorithm ◽

Tracking Error ◽

Iterative Learning ◽

Consensus Control ◽

Partial Difference ◽

Consensus Tracking ◽

Fixed Topology ◽

Virtual Leader

This paper considers the consensus control problem of nonlinear spatial-temporal hyperbolic partial difference multiagent systems and parabolic partial difference multiagent systems with time delay. Based on the system’s own fixed topology and the method of generating the desired trajectory by introducing virtual leader, using the consensus tracking error between the agent and the virtual leader agent and neighbor agents in the last iteration, an iterative learning algorithm is proposed. The sufficient condition for the system consensus error to converge along the iterative axis is given. When the iterative learning number k approaches infinity, the consensus error in the sense of the L 2 norm between all agents in the system will converge to zero. Furthermore, simulation results illustrate the effectiveness of the algorithm.

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Consensus Tracking Via Iterative Learning Control for Singular Fractional-Order Multi-Agent Systems Under Iteration-Varying Topologies and Initial State Errors

IEEE Access ◽

10.1109/access.2020.3023908 ◽

2020 ◽

Vol 8 ◽

pp. 168812-168824

Author(s):

Jingjing Wang ◽

Jiaquan Zhou ◽

Yajing Mo ◽

Linxin Li

Keyword(s):

Fractional Order ◽

Iterative Learning Control ◽

Learning Control ◽

Iterative Learning ◽

Multi Agent Systems ◽

Initial State ◽

Agent Systems ◽

Consensus Tracking ◽

Multi Agent

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Consensus Control of Multi-agent Robot System with State Delay Based on Fractional-Order Iterative Learning Control Algorithm

Journal Européen des Systèmes Automatisés ◽

10.18280/jesa.530603 ◽

2020 ◽

Vol 53 (6) ◽

pp. 771-779

Author(s):

Yanghua Gao ◽

Weidong Lou ◽

Hailiang Lu ◽

Yonghua Jia

Keyword(s):

Fractional Order ◽

Finite Time ◽

Iterative Learning Control ◽

Learning Control ◽

Iterative Learning ◽

Robot System ◽

Consensus Control ◽

Repetitive Motion ◽

Multi Agent ◽

Fixed Topology

This paper mainly explores the consensus control of multi-agent robot system with repetitive motion under the constraints of a leader and fixed topology. To realize the consensus control, a fractional order iterative learning control (FOILC) algorithm was designed under the mode of distributed open-closed-loop proportional-derivative alpha (PDα). The uniform convergence of the algorithm in finite time was discussed, drawing on factional calculus, graph theory, and norm theory, resulting in the convergence conditions. Theoretical analysis shows that, with the growing number of iterations, each agent can choose the appropriate gain matrix, and complete the tracking task in finite time. The effectiveness of the proposed method was verified through simulation.

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