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.

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.

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 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.

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.

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.

An iterative learning control algorithm based on time varying pilot factor

2019 ◽  
Vol 25 (8) ◽  
pp. 1484-1491 ◽  
Author(s):  
Jing Huang ◽  
Zhenxiang Xu ◽  
Guoxiu Li ◽  
Cheng Qiu ◽  
Haitao Huang
Keyword(s):  
Control System ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Sufficient Conditions ◽  
Learning Control ◽  
Critical Issue ◽  
Iterative Learning ◽  
Time Varying ◽  
Initial State ◽  
Hydraulic Servo

Owing to the control system being repetitive and nonlinear, a time-varying pilot factor control algorithm based on iterative learning control is proposed. The convergence of the TPF-ILC control algorithm is mathematically proven and the sufficient conditions are given. Thereafter, the initial state issue of iterative learning is explored, which is the critical issue of iterative learning control. The convergence of the system’s control error and the initial state of every single period have been mathematically proved by using continuous and repetitive properties of the system, even if the initial states of every single iterative learning period are not strictly the same. At the end of this paper, the TPF-ILC algorithm is applied in a hydraulic servo control system, and experimental results indicate the effectiveness and practicability of the TPF-ILC 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 RBFNN-Based Nonuniform Trajectory Tracking Adaptive Iterative Learning Control for Uncertain Nonlinear System with Continuous Nonlinearly Input

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Chunli Zhang ◽  
Xu Tian ◽  
Lei Yan
Keyword(s):  
Nonlinear System ◽  
Iterative Learning Control ◽  
Tracking Error ◽  
Learning Control ◽  
Convergent Series ◽  
Iterative Learning ◽  
Time Interval ◽  
Uncertain Nonlinear System ◽  
Initial State ◽  
Adaptive Iterative Learning Control

This paper proposes an adaptive iterative learning control (AILC) method for uncertain nonlinear system with continuous nonlinearly input to solve different target tracking problem. The method uses the radial basis function neural network (RBFNN) to approximate every uncertain term in systems. A time-varying boundary layer, a typical convergent series are introduced to deal with initial state error and unknown bounds of errors, respectively. The conclusion is that the tracking error can converge to a very small area with the number of iterations increasing. All closed-loop signals are bounded on finite-time interval 0 , T . Finally, the simulation result of mass-spring mechanical system shows the correctness of the theory and validity of the method.

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