P-type iterative learning control algorithm for a class of linear singular impulsive systems

Liu, Qian; Tian, Senping; Gu, Panpan

doi:10.1016/j.jfranklin.2018.03.011

Cited by 25 publications

(12 citation statements)

References 23 publications

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“…By means of denotations (18)-(21), the equation (23) converts into Equivalently, the equation 24becomes…”

Section: Solution Of the Optimized-gain Vector And The Linearly mentioning

confidence: 99%

“…Following up the ILC investigations for ordinary systems purely described by difference or differential equations, the ILC studies for singular systems have earned many efforts covering an open and a closed-loop ILC technique using the standard dynamic decomposition, the asymptotic convergence in the sense of lambda-norm measurement [19], [20] a closed-loop PD-type ILC technique via an initial state rectification [21], a D-type ILC handling random initial states [22], the P-type ILCs for singular impulsive system and distributed parameter systems [23], [24] and an iterative learning controller with packet loss [25] and so on.…”

Section: Introductionmentioning

confidence: 99%

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Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems

et al. 2021

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In this article, the repetitive finite-length linear discrete-time singular system is formulated as an input-output equation by virtue of the lifted-vector method and a gain-optimized P-type iterative learning control profile is architected by sequentially arguing the learning-gain vector in minimizing the addition of the quadratic norm of the tracking-error vector and the weighed quadratic norm of the compensation vector. By virtue of the elementary permutation matrix and the property of the quadratic function, the optimized-gain vector is solved and explicitly expressed by the system Markov matrix and the iterationwise tracking error. Then the linearly monotonic convergence of the tracking error is derived under the assumption that the initial state of the dynamic subsystem is resettable. Furthermore, for the circumstance that the system parameters uncertainties exist, the quasi scheme is established by replacing the exact system Markov matrix with the approximated one in the optimized gain. Rigorous analysis conveys that the proposed gain-optimized scheme is robust to the system internal disturbance within a suitable range. The validity and effectiveness are demonstrated numerically. INDEX TERMS Discrete-time singular systems, iterative learning control, linearly monotonic convergence, robustness, the optimized-gain vector, tuning factor.

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“…By means of denotations (18)-(21), the equation (23) converts into Equivalently, the equation 24becomes…”

Section: Solution Of the Optimized-gain Vector And The Linearly mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems

et al. 2021

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“…Over the last two decades, this technique has been the center of interest of many researchers. [2][3][4][5][6][7][8][9][10][11][12][13][14][15] dead-zone may severely degrade system performance. How to deal with these uncertainties becomes another direction in the development of ILC.…”

Section: Introductionmentioning

confidence: 99%

“…In this approach, the input of controlled system in current cycle is modified by applying the proportional strategy on the error achieved between the system output and the desired trajectory in a last previous iteration. P-type iterative learning scheme was studies recently for the control systems, for example, in Reference [2], a P-type ILC algorithm was applied for a class of linear singular impulsive systems. The monotonic convergence property of P-type learning controller was designed for a class of discrete-time systems in References [24,25].…”

Section: Introductionmentioning

confidence: 99%

Adaptive P‐type iterative learning radial basis function control for robot manipulators with unknown varying disturbances and unknown input dead zone

Bensidhoum

Bouakrif

2020

Intl J Robust & Nonlinear

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This article proposes an adaptive iterative learning radial basis function (RBF) scheme to solve the trajectory-tracking problem for perturbed robot manipulators with unknown iteration varying disturbances and unknown dead-zone input. It is well known that the presence of the dead zone in actuators and mechatronics devices gives rise to extra difficulty due to the presence of singularity in the input channels. Hence, it is interesting to take this problem into account when synthesizing a controller. This synthesis is made here. In addition, the control design is very simple in the sense that we use, only, the proportional gain. Therefore, the considerable amount noise caused by the sensors for velocity measurements of robot manipulators is avoided. Another advantage of this work is that the unknown disturbances are assumed to be time varying and also varying from iteration to iteration. Thus, the RBF neural network is used to approximate these unknown nonlinear functions. Using the Lyapunov theory, the analysis of the stability of the closed-loop system is guaranteed when the iteration number tends to infinity. Finally, simulation results on the PUMA 560 arm are provided to illustrate the effectiveness of the proposed method. In order to evaluate the performance of our controller, a comparison of our results with other method is also given. K E Y W O R D SIterative learning control, Radial basis function, Dead-zone, Adaptive, Robot manipulators, Lyapunov theory 1 Indeed, input uncertainties such as dead-zone, saturation, backlash, and hysteresis are kind of nonsmooth and nonaffine in input factor widely existing in actuators and sensors. In fact, in many practical applications, the presence of Int J Robust Nonlinear Control. 2020;30:4075-4094.wileyonlinelibrary.com/journal/rnc

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“…Since the early work of Arimoto et al (1984), this technique has been the center of interest for many researchers over the last decades (see, for instance Ardakani et al, 2017; Bouakrif, 2010; Bouakrif, 2011a; Bouakrif, 2011c; Bouakrif and Zasadzinski, 2016; Bouakrif and Zasadzinski, 2018; Bouakrif et al, 2013; Devasia, 2016; Li et al, 2016; Liang and Wang, 2018; Liu et al, 2017; Meng and Moore, 2017; Zundert et al, 2016). In fact, according to the learning action type, there are mainly four schemes of ILC: P-type (Liu et al, 2018), D-type (Bouakrif, 2011b; Dai et al, 2018), PD-type (Park, 2005) and PID-type (Madady, 2008). In addition, ILC has been widely used in industries such as robots industrial (Tayebi and Islam, 2006), hard disk drive (Chen et al, 2006), multi-agent systems (Jin, 2016) and piezo nanopositioner (Feng et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Iterative learning radial basis function neural networks control for unknown multi input multi output nonlinear systems with unknown control direction

Bensidhoum

Bouakrif

Zasadzinski

2019

Transactions of the Institute of Measurement and Control

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In this paper, an iterative learning radial basis function neural-networks (RBF NN) control algorithm is developed for a class of unknown multi input multi output (MIMO) nonlinear systems with unknown control directions. The proposed control scheme is very simple in the sense that we use just a P-type iterative learning control (ILC) updating law in which an RBF neural network term is added to approximate the unknown nonlinear function, and an adaptive law for the weights of RBF neural network is proposed. We chose the RBF NN because it has universal approximation capabilities and can approximate any continuous function. In addition, among the advantages of our controller scheme is the fact that it is applicable to deal with a class of nonlinear systems without the need to satisfy the global Lipschitz continuity condition and we assume, only, that the unstructured uncertainty is norm-bounded by an unknown function. Another advantage of the proposed controller and unlike other works on ILC, we do not need any prior knowledge of the control directions for MIMO nonlinear system. Thus, the Nussbaum-type function is used to solve the problem of unknown control directions. In order to prove the asymptotic stability of the closed-loop system, a Lyapunov-like positive definite sequence is used, which is shown to be monotonically decreasing under the control design scheme. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control scheme.

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P-type iterative learning control algorithm for a class of linear singular impulsive systems

Cited by 25 publications

References 23 publications

Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems

Linearly Monotonic Convergence and Robustness of P-Type Gain-Optimized Iterative Learning Control for Discrete-Time Singular Systems

Adaptive P‐type iterative learning radial basis function control for robot manipulators with unknown varying disturbances and unknown input dead zone

Iterative learning radial basis function neural networks control for unknown multi input multi output nonlinear systems with unknown control direction

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