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

Bensidhoum, Tarek; Bouakrif, Farah; Zasadzinski, Michel

doi:10.1177/0142331219826659

Cited by 9 publications

(12 citation statements)

References 49 publications

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“…Besides, it is obvious that P is equal to P opt while selecting the variables as (22). Hence, P opt is the optimal covariance matrix and the optimal variables are presented in (22), which completes the proof. □ Remark 3.…”

Section: Theorem 1 the Lower Bound Of P Which Is Denoted As Pmentioning

confidence: 62%

Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

Huang

Yang

Zhu

et al. 2021

IET Control Theory & Appl

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Feedforward control has been widely used to improve the tracking performance of precision motion systems. This paper develops a new data-driven feedforward tuning approach associated with rational basis functions. The aim is to obtain the global optimum with optimal estimation accuracy. First, the instrumental variable is employed to ensure the unbiased estimation of the global optimum. Then, the optimal instrumental variable which leads to the highest estimation accuracy is derived, and a new refined instrumental variable method is exploited to estimate the optimal instrumental variable. Moreover, the estimation accuracy of the optimal parameter is further improved through the proposed parameter updating law. Simulations are conducted to test the parameter estimation accuracy of the proposed approach, and it is demonstrated that the global optimum is unbiasedly estimated with optimal parameter estimation accuracy in terms of variance with the proposed approach. Experiments are performed and the results validate the excellent performance of the proposed approach for varying tasks. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Theorem 1 the Lower Bound Of P Which Is Denoted As Pmentioning

confidence: 62%

Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

Huang

Yang

Zhu

et al. 2021

IET Control Theory & Appl

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“…This is because in ILC two independent variables exist, where one of the variables is time and the other one is repetition number. The interested readers are referred to Ahn et al (2007), Xu (2011), Bouakrif and Zasadzinski (2018), Shen (2018), Afsharnia et al (2019), Bensidhoum et al (2019), Jonnalagadda et al (2020) and references therein in order to see the concepts and applications of ILC, and see Geng et al (1990), Owens et al (2000), Li et al (2005a), Hladowski et al (2010), Meng et al (2010), Guan et al (2014) and Wang et al (2017b) for the usage of 2-D systems theory in ILC design.…”

Section: Application To the Ilc Designmentioning

confidence: 99%

Stabilization of two-dimensional mixed continuous-discrete-time systems via dynamic output feedback with application to iterative learning control design

Asl

Madady

2021

Transactions of the Institute of Measurement and Control

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This paper investigates the asymptotic stabilization of the 2-D continuous-discrete-time systems via dynamic output feedback. The problem is formulated in a general framework, where the system and controller are both described by the Roesser model. By rigorous mathematical works, a linear matrix inequality (LMI) condition is established to ensure the asymptotic stability of the closed-loop system. Using this LMI condition, the problem of determining the stabilizing controller parameters is converted to a rank minimization problem (RMP) with an LMI constraint, or equivalently to a rank-constrained optimization problem (RCOP). When this RMP (or equivalently this RCOP) has a solution, then the controller parameters are obtained uniquely by an explicit formula in terms of this solution. Moreover, it is shown that one can transform the problem of one-dimensional continuous-time iterative learning control (ILC) design to a 2-D stabilization problem, and consequently solve it using the presented two-dimensional scheme. Some numerical examples are given to illustrate the proposed method.

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“…2. Unlike many works based on ILC, 3,14,40 where the disturbances are supposed to be invariant, in our article, these disturbances are supposed to be nonrepetitive and also unknown. 3.…”

Section: Introductionmentioning

confidence: 96%

“…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%

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

Cited by 9 publications

References 49 publications

Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

Stabilization of two-dimensional mixed continuous-discrete-time systems via dynamic output feedback with application to iterative learning control design

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

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