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.

scholarly journals Adaptive Iterative Learning Control for Complex Dynamical Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Xiuqing Hao ◽  
Junmin Li
Keyword(s):  
Iterative Learning Control ◽  
Tracking Error ◽  
Reference Signal ◽  
Learning Control ◽  
Iterative Learning ◽  
Complex Dynamical Networks ◽  
Time Interval ◽  
Adaptive Iterative Learning Control ◽  
Dynamical Networks ◽  
Composite Energy

A new adaptive iterative learning control scheme is proposed for complex dynamical networks with repetitive operation over a fixed time interval. By designing difference type updating laws for unknown time-varying parameters and coupling strength, the state of each node in complex dynamical networks can track the reference signal. By constructing a composite energy function, a sufficient condition of the convergence of tracking error sequence is achieved in the iteration domain. Finally, a numerical example is given to show the effectiveness of the designed 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.

D-type iterative learning control without resetting condition for robot manipulators

Robotica ◽  
2011 ◽  
Vol 29 (7) ◽  
pp. 975-980 ◽  
Author(s):  
Farah Bouakrif
Keyword(s):  
Iterative Learning Control ◽  
Robot Manipulators ◽  
Learning Control ◽  
Iterative Learning ◽  
Time Interval ◽  
Initial State ◽  
External Disturbances ◽  
Repetitive Tasks ◽  
Control Scheme ◽  
Topological Measure

SUMMARYThis paper deals with iterative learning control (ILC) design to solve the trajectory tracking problem for rigid robot manipulators subject to external disturbances, and performing repetitive tasks. A D-type ILC is presented with an initial condition algorithm, which gives the initial state value in each iteration automatically. Thus, the resetting condition (the initial state error is equal to zero) is not required. The λ-norm is adopted as the topological measure in our proof of the asymptotic stability of this control scheme, over the whole finite time-interval, when the iteration number tends to infinity. Simulation results are presented to illustrate the effectiveness of the proposed control scheme.

Adaptive Iterative Learning Control for Nonlinear Systems With Unknown Control Gain1

2004 ◽  
Vol 126 (4) ◽  
pp. 916-920 ◽  
Author(s):  
Huadong Chen ◽  
Ping Jiang
Keyword(s):  
Nonlinear Systems ◽  
Iterative Learning Control ◽  
Control Method ◽  
Learning Control ◽  
Iterative Learning ◽  
Time Interval ◽  
Learning Gain ◽  
Adaptive Iterative Learning Control ◽  
Control Gain ◽  
Unknown Control

An adaptive iterative learning control approach is proposed for a class of single-input single-output uncertain nonlinear systems with completely unknown control gain. Unlike the ordinary iterative learning controls that require some preconditions on the learning gain to stabilize the dynamic systems, the adaptive iterative learning control achieves the convergence through a learning gain in a Nussbaum-type function for the unknown control gain estimation. This paper shows that all tracking errors along a desired trajectory in a finite time interval can converge into any given precision through repetitive tracking. Simulations are carried out to show the validity of the proposed control method.

Adaptive Iterative Learning Control for Robot Manipulators with Initial Resetting Errors

2011 ◽  
Vol 130-134 ◽  
pp. 265-269 ◽  
Author(s):  
Jian Ming Wei ◽  
Yun An Hu
Keyword(s):  
Iterative Learning Control ◽  
Robot Manipulators ◽  
Error Function ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Unknown Parameters ◽  
Adaptive Iterative Learning Control ◽  
Suitable Parameter ◽  
Parameter Values

In this paper, an adaptive iterative learning control is presented for robot manipulators with unknown parameters, performing repetitive tasks. In order to overcome the initial resetting errors, an auxiliary tracking error function is introduced. The adaptive algorithm is derived along the iteration axis to search for suitable parameter values. The technical analysis shows convergence of the tracking errors. Finally, simulation results are provided to illustrate the effectiveness of the proposed controller.

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.

Backstepping Adaptive Iterative Learning Control for Robotic Systems

2013 ◽  
Vol 284-287 ◽  
pp. 1759-1763
Author(s):  
Ying Chung Wang ◽  
Chiang Ju Chien ◽  
Chi Nan Chuang
Keyword(s):  
Neural Network ◽  
Iterative Learning Control ◽  
Fuzzy Neural Network ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Robotic Systems ◽  
Adaptive Iterative Learning Control ◽  
Repetitive Tasks ◽  
Fuzzy Neural

A backstepping adaptive iterative learning control for robotic systems with repetitive tasks is proposed in this paper. The backstepping-like procedure is introduced to design the AILC. A fuzzy neural network is applied for compensation of the unknown certainty equivalent controller. Using a Lyapunov like analysis, we show that the adjustable parameters and internal signals remain bounded, the tracking error will asymptotically converge to zero as iteration goes to infinity.

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.

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