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.

Consensus Tracking in Multi-Node Systems Using Iterative Learning Control Based on Delay Exponential Matrix

2018 ◽  
Vol 06 (03) ◽  
pp. 209-219 ◽  
Author(s):  
Zijian Luo ◽  
Wenjun Xiong ◽  
Xinghuo Yu
Keyword(s):  
Iterative Learning Control ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Learning Control ◽  
Iterative Learning ◽  
Consensus Tracking ◽  
Operating Environments ◽  
Representation Of Solutions ◽  
Delay Differential ◽  
Exponential Matrix

By using the representation of solutions of delay differential equation involving delayed exponential matrix, we study finite-time consensus convergence of iterative learning control for multi-node systems with time-delays in repeatable operating environments with a fixed and directed communication topology and delay. Sufficient conditions for both iteration-invariant and iteration-varying consensus tracking trajectories are given to guarantee the convergence of consensus tracking error in the sense of [Formula: see text]-norm. Finally, numerical examples are given to verify the theoretical results.

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.

scholarly journals New Iterative Learning Control Algorithm Using Learning Gain Based on σ Inversion for Nonsquare Multi-Input Multi-Output Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Leila Noueili ◽  
Wassila Chagra ◽  
Moufida Ksouri
Keyword(s):  
Iterative Learning Control ◽  
Mimo Systems ◽  
Linear Time ◽  
Tracking Error ◽  
Learning Control ◽  
Convergence Condition ◽  
Iterative Learning ◽  
Learning Gain ◽  
Model Inversion ◽  
Direct Model

Model inversion Iterative Learning Control (ILC) for a class of nonsquare linear time variant/invariant multi-input multi-output (MIMO) systems is considered in this paper. A new ILC algorithm is developed based on σ-right inversion of nonsquare learning gain matrices to resolve the matrix inversion problems appeared in the direct model inversion of nonsquare MIMO systems. Furthermore, a sufficient and necessary monotonic convergence condition is established. With rigorous analysis, the proposed ILC scheme guarantees the convergence of the tracking error. To prove the effectiveness and to illustrate the performance of the proposed approach for linear time-invariant (LTI) and time-varying nonsquare systems, two illustrative examples are simulated.

scholarly journals An Accelerated Error Convergence Design Criterion and Implementation of Lebesgue-p Norm ILC Control Topology for Linear Position Control Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Saleem Riaz ◽  
Hui Lin ◽  
Muhammad Waqas ◽  
Farkhanda Afzal ◽  
Kai Wang ◽  
...  
Keyword(s):  
Iterative Learning Control ◽  
Control Algorithm ◽  
Position Control ◽  
Tracking Error ◽  
Learning Control ◽  
Convergence Condition ◽  
Design Criterion ◽  
Iterative Learning ◽  
Current Error ◽  
P Type

Traditional and typical iterative learning control algorithm shows that the convergence rate of error is very low for a class of regular linear systems. A fast iterative learning control algorithm is designed to deal with this problem in this paper. The algorithm is based on the traditional P-type iterative learning control law, which increases the composition of adjacent two overlapping quantities, the tracking error of previous cycle difference signals, and the current error difference. Using convolution to promote Young inequalities proved strictly that, in terms of Lebesgue-p norm, when the number of iterations tends to infinity, the tracking error converges to zero in the system and presents the convergence condition of the algorithm. Compared with the traditional P-type iterative learning control algorithm, the proposed algorithm improves convergence speed and evades the defect using the norm metric’s tracking error. Finally, the validation of the effectiveness of the proposed algorithm is further proved by simulation results.

Iterative learning control algorithm for sensor fault nonlinear systems

2020 ◽  
pp. 1-8
Author(s):  
Zimian Lan
Keyword(s):  
Nonlinear Systems ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Tracking Error ◽  
Learning Control ◽  
Open Loop ◽  
Iterative Learning ◽  
Sensor Fault ◽  
Initial State ◽  
Control Gain

In this paper, we propose a new iterative learning control algorithm for sensor faults in nonlinear systems. The algorithm does not depend on the initial value of the system and is combined with the open-loop D-type iterative learning law. We design a period that shortens as the number of iterations increases. During this period, the controller corrects the state deviation, so that the system tracking error converges to the boundary unrelated to the initial state error, which is determined only by the system’s uncertainty and interference. Furthermore, based on the λ norm theory, the appropriate control gain is selected to suppress the tracking error caused by the sensor fault, and the uniform convergence of the control algorithm and the boundedness of the error are proved. The simulation results of the speed control of the injection molding machine system verify the effectiveness of the algorithm.

A data-driven approach for trajectory-based aircraft operation with controlled time of arrival and along-track wind effects

2020 ◽  
Vol 42 (12) ◽  
pp. 2166-2177
Author(s):  
Gaoyang Jiang ◽  
Zhongsheng Hou
Keyword(s):  
Control Problem ◽  
Iterative Learning Control ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Data Driven ◽  
Time Of Arrival ◽  
Multiple Time ◽  
Data Driven Approach ◽  
Along Track

Trajectory-based aircraft operation and control is one of the hot issues in air traffic management. However, the accurate mechanism modeling of aircraft is tough work, and the operation data have not been effectively utilized in many studies. So, in this work, we apply the model-free adaptive iterative learning control method to address the time-of-arrival control problem in trajectory-based aircraft operation. This problem is first formulated into a trajectory tracking problem with along-track wind disturbance. Through rigorous analysis, it is shown that this method, combined with point-to-point iterative learning control (ILC) strategy, can effectively deal with the arrival time control problem with multiple time constraints. Then, the terminal ILC strategy is applied, aiming to resolve the same problem with a time constraint at the end point. Compared with the PID (Proportional Integral Derivative) type ILC, the proposed method improves control performance by 11.15% in root mean square of tracking error and 9.32% in integral time absolute error. The sensitivity and flexibility of the data-driven approach is further verified through numerical simulations.

Sign in / Sign up

Export Citation Format

Share Document