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

Complexity ◽  
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.

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

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Shuaishuai Lv ◽  
Mian Pan ◽  
Xungen Li ◽  
Qi Ma ◽  
Tianyi Lan ◽  
...  
Keyword(s):  
Multiagent Systems ◽  
Fractional Order ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Convergence Conditions ◽  
Consensus Tracking ◽  
Communication Topology ◽  
Fixed Topology ◽  
Virtual Leader

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.

Rapid iterative learning algorithm of nonlinear time-delay system with initial deviation

2020 ◽  
pp. 002072092094057
Author(s):  
Xiaoyan Cheng ◽  
Hongbin Wang ◽  
Qinzhao Wang ◽  
Shaochan Feng
Keyword(s):  
Time Delay ◽  
Trajectory Tracking ◽  
Learning Algorithm ◽  
Tracking Error ◽  
Iterative Learning ◽  
Forgetting Factor ◽  
Initial State ◽  
Trajectory Tracking Control ◽  
Joint Rotation ◽  
Variable Forgetting Factor

A rapid iterative learning control algorithm with variable forgetting factor is applied for a class of nonlinear system with initial error and time-delay. This algorithm eliminats the limitation that the initial state should be reset to the expected one or fixed value at the start of iteration in the learning process of conventional algorithms. The error and the differences between two adjacent error is adopted to correct the controller avoiding the unstable influence of the derivative for PD type algorithm and the available information is fully used to increase convergence rate. Furthermore variable forgetting factor introduced guaranteed a fast convergence of trajectory tracking error Then, with applying the rapid algorithm to the trajectory tracking control of manipulator, the learning speed and tracking performance are both greatly improved. Meanwhile, the control strategy is proposed for the limitation of each joint rotation. The convergence of the method is also proved theoretically. Finally, simulation results illustrates the effectiveness and the real-time ability of the proposed way.

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

Algorithms ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 185 ◽  
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.

Iterative learning algorithm with a quadratic criterion for linear time-varying systems

2002 ◽  
Vol 216 (3) ◽  
pp. 309-316 ◽  
Author(s):  
S N Huang ◽  
K K Tan ◽  
T H Lee
Keyword(s):  
Learning Algorithm ◽  
Linear Time ◽  
Tracking Error ◽  
Iterative Learning ◽  
Tracking Performance ◽  
Time Varying ◽  
Control Scheme ◽  
Time Varying Systems ◽  
Simulation Results ◽  
Learning Law

A novel iterative learning controller for linear time-varying systems is developed. The learning law is derived on the basis of a quadratic criterion. This control scheme does not include package information. The advantage of the proposed learning law is that the convergence is guaranteed without the need for empirical choice of parameters. Furthermore, the tracking error on the final iteration will be a class K function of the bounds on the uncertainties. Finally, simulation results reveal that the proposed control has a good setpoint tracking performance.

scholarly journals Distributed Consensus Tracking for Second-Order Nonlinear Multiagent Systems with a Specified Reference State

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Guoguang Wen ◽  
Yongguang Yu ◽  
Zhaoxia Peng ◽  
Ahmed Rahmani
Keyword(s):  
Multiagent Systems ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lyapunov Theory ◽  
Reference Trajectory ◽  
Distributed Consensus ◽  
Consensus Tracking ◽  
Velocity Information ◽  
Virtual Leader

This paper mainly addresses the distributed consensus tracking problem for second-order nonlinear multiagent systems with a specified reference trajectory. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position and velocity information of its neighbors. The consensus reference is taken as a virtual leader, whose output is only its position and velocity information that is available to only a subset of a group of followers. To achieve consensus tracking, a class of nonsmooth control protocols is proposed which reply on the relative information among the neighboring agents. Then some corresponding sufficient conditions are derived. It is shown that if the communication graph associated with the virtual leader and followers is connected at each time instant, the consensus can be achieved at least globally exponentially with the proposed protocol. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Finally, numerical examples are presented to illustrate the theoretical analysis.

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