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 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 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.

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.

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.

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.

scholarly journals Output Information Based Fault-Tolerant Iterative Learning Control for Dual-Rate Sampling Process with Disturbances and Output Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Hongfeng Tao ◽  
Yan Liu ◽  
Huizhong Yang
Keyword(s):  
Iterative Learning Control ◽  
Fault Tolerant ◽  
Sampling Rate ◽  
Sufficient Conditions ◽  
Learning Control ◽  
Iterative Learning ◽  
Repetitive Process ◽  
Sampling Process ◽  
Output Delay ◽  
Output Information

For a class of single-input single-output (SISO) dual-rate sampling processes with disturbances and output delay, this paper presents a robust fault-tolerant iterative learning control algorithm based on output information. Firstly, the dual-rate sampling process with output delay is transformed into discrete system in state-space model form with slow sampling rate without time delay by using lifting technology; then output information based fault-tolerant iterative learning control scheme is designed and the control process is turned into an equivalent two-dimensional (2D) repetitive process. Moreover, based on the repetitive process stability theory, the sufficient conditions for the stability of system and the design method of robust controller are given in terms of linear matrix inequalities (LMIs) technique. Finally, the flow control simulations of two flow tanks in series demonstrate the feasibility and effectiveness of the proposed method.

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