scholarly journals PDα-type iterative learning control with initial state learning for fractional-order systems

2021 ◽  
Vol 39 (2) ◽  
pp. 400-406
Author(s):  
Fen Liu ◽  
Kejun Zhang
Keyword(s):  
Fractional Order ◽  
Iterative Learning Control ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Learning Control ◽  
Young Inequality ◽  
Iterative Learning ◽  
Initial State ◽  
Arbitrary Initial State ◽  
State Learning

In order to eliminate the influence of the arbitrary initial state on the systems, open-loop and open-close-loop PDα-type fractional-order iterative learning control (FOILC) algorithms with initial state learning are proposed for a class of fractional-order linear continuous-time systems with an arbitrary initial state. In the sense of Lebesgue-p norm, the sufficient conditions for the convergence of PDα-type algorithms are disturbed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral. The results demonstrate that under these novel algorithms, the convergences of the tracking error are can be guaranteed. Numerical simulations support the effectiveness and correctness of the proposed algorithms.

scholarly journals Fractional-order iterative learning control for robotic Arm-PD2Dα type

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 1-10
Author(s):  
Bosko Cvetkovic ◽  
Mihailo Lazarevic
Keyword(s):  
Fractional Order ◽  
Iterative Learning Control ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Learning Control ◽  
Joint Space ◽  
Open Loop ◽  
Iterative Learning ◽  
Robotic Arm ◽  
Trajectory Tracking Control

In this paper, a new open-loop PD2D? type a fractional order iterative learning control (ILC) is studied for joint space trajectory tracking control of a linearized uncertain robotic arm. The robust convergent analysis of the tracking errors has been done in time domain where it is theoretically proven that the boundednesses of the tracking error are guaranteed in the presence of model uncertainty. The convergence of the proposed open-loop ILC law is proven mathematically using Gronwall integral inequality for a linearized robotic system and sufficient conditions for convergence and robustness are obtained.

scholarly journals ILC for Non-Linear Hyperbolic Partial Difference Systems

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3076
Author(s):  
Meryem Hamidaoui ◽  
Cheng Shao
Keyword(s):  
Iterative Learning Control ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Learning Control ◽  
Iterative Learning ◽  
Monotone Convergence ◽  
Initial State ◽  
Partial Difference ◽  
Gronwall’S Inequality ◽  
Non Linear

This paper discusses the iterative learning control problem for a class of non-linear partial difference system hyperbolic types. The proposed algorithm is the PD-type iterative learning control algorithm with initial state learning. Initially, we introduced the hyperbolic system and the control law used. Subsequently, we presented some dilemmas. Then, sufficient conditions for monotone convergence of the tracking error are established under the convenient assumption. Furthermore, we give a detailed convergence analysis based on previously given lemmas and the discrete Gronwall’s inequality for the system. Finally, we illustrate the effectiveness of the method using a numerical example.

scholarly journals The Effect of Initial State Error for Nonlinear Systems with Delay via Iterative Learning Control

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Zhang Qunli
Keyword(s):  
Nonlinear Systems ◽  
Iterative Learning Control ◽  
Time Delays ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Learning Control ◽  
Iterative Learning ◽  
The Novel ◽  
Initial State ◽  
Initial States

An iterative learning control problem for nonlinear systems with delays is studied in detail in this paper. By introducing theλ-norm and being inspired by retarded Gronwall-like inequality, the novel sufficient conditions for robust convergence of the tracking error, whose initial states are not zero, with time delays are obtained. Finally, simulation example is given to illustrate the effectiveness of the proposed method.

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

Complexity ◽  
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.

D-type iterative learning control for a class of parabolic partial difference systems

2018 ◽  
Vol 40 (10) ◽  
pp. 3105-3114 ◽  
Author(s):  
Xisheng Dai ◽  
Sange Mei ◽  
Senping Tian ◽  
Ling Yu
Keyword(s):  
Iterative Learning Control ◽  
Closed Loop ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Learning Control ◽  
Open Loop ◽  
Iterative Learning ◽  
Initial State ◽  
Partial Difference ◽  
Difference Systems

In this paper, an iterative learning control problem is addressed for a class of parabolic partial difference systems. Several discrete D-type iterative learning control algorithms with initial state learning are proposed for the systems which have no direct channel between the input and output as well as the initial state value being unfixed in the learning process. Based on fundamental mathematical analysis tools and the discrete Gronwall inequality, sufficient conditions for tracking error convergence in the iterative domain for open-loop, closed-loop and open-closed-loop iterative learning control are established and proven respectively. Numerical simulations verify the effectiveness of the theoretical 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.

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