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.

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.

Iterative Learning Control With Switching Gain Feedback for Nonlinear Systems

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
P. R. Ouyang ◽  
B. A. Petz ◽  
F. F. Xi
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Iterative Learning Control ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Trajectory Tracking Control ◽  
Control Scheme

Iterative learning control (ILC) is a simple and effective technique of tracking control aiming at improving system tracking performance from trial to trial in a repetitive mode. In this paper, we propose a new ILC called switching gain PD-PD (SPD-PD)-type ILC for trajectory tracking control of time-varying nonlinear systems with uncertainty and disturbance. In the developed control scheme, a PD feedback control with switching gains in the iteration domain and a PD-type ILC based on the previous iteration combine together into one updating law. The proposed SPD-PD ILC takes the advantages of feedback control and classical ILC and can also be viewed as online-offline ILC. It is theoretically proven that the boundednesses of the state error and the final tracking error are guaranteed in the presence of uncertainty, disturbance, and initialization error of the nonlinear systems. The convergence rate is adjustable by the adoption of the switching gains in the iteration domain. Simulation experiments are conducted for trajectory tracking control of a nonlinear system and a robotic system. The results show that fast convergence and small tracking error bounds can be observed by using the SPD-PD-type ILC.

scholarly journals Research on Open-Closed-Loop Iterative Learning Control with Variable Forgetting Factor of Mobile Robots

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Hongbin Wang ◽  
Jian Dong ◽  
Yueling Wang
Keyword(s):  
Mobile Robot ◽  
Iterative Learning Control ◽  
Closed Loop ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Learning Control ◽  
Iterative Learning ◽  
Forgetting Factor ◽  
Output Measurement ◽  
Variable Forgetting Factor

We propose an iterative learning control algorithm (ILC) that is developed using a variable forgetting factor to control a mobile robot. The proposed algorithm can be categorized as an open-closed-loop iterative learning control, which produces control instructions by using both previous and current data. However, introducing a variable forgetting factor can weaken the former control output and its variance in the control law while strengthening the robustness of the iterative learning control. If it is applied to the mobile robot, this will reduce position errors in robot trajectory tracking control effectively. In this work, we show that the proposed algorithm guarantees tracking error bound convergence to a small neighborhood of the origin under the condition of state disturbances, output measurement noises, and fluctuation of system dynamics. By using simulation, we demonstrate that the controller is effective in realizing the prefect tracking.

scholarly journals Adaptive Trajectory Tracking Control of a Quadrotor Based on Iterative Learning Algorithm

2018 ◽  
Author(s):  
Mohammad Mehdi Farzaneh ◽  
Alireza Tavakolpour-Saleh
Keyword(s):  
Trajectory Tracking ◽  
Pid Control ◽  
Tracking Control ◽  
Control Method ◽  
Learning Algorithm ◽  
Optimal Algorithm ◽  
Adaptive Method ◽  
Iterative Learning ◽  
Trajectory Tracking Control ◽  
Control Loops

This paper presents a new adaptive and optimal algorithm for the trajectory tracking control of a quadrotor using iterative learning algorithm (ILA) and enumerative learning algorithm. Ordinarily the ILA, as an adaptive method, can perform well with PID control to improve the controller’s performance for a nonlinear system. Quadrotors are considered as non-linear and unstable systems which the use of an adaptive and optimal controller can increase its stability and decrease error level. In this method, a PID controller is proposed for the outer and inner control loops of a quadrotor and the ILA is used to adapt PID control gains. Subsequently, an enumerative learning algorithm is used to optimize the learning rates of the ILA. For this purpose, at first, the dynamic model of the quadrotor is acquired. After that, the structure of the inner and outer control loops is defined. In the end, the simulation results for the trajectory tracking control of a quadrotor are demonstrated. Through simulation, it is concluded that as time increases, the performance of the suggested control method in trajectory tracking control becomes better and better and error signals convergence to zero.

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.

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.

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