Dynamic multivariate B-spline neural network design using orthogonal least squares algorithm for non-linear system identification

Mirea, Letitia

doi:10.1109/icstcc.2014.6982503

Cited by 6 publications

(3 citation statements)

References 12 publications

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“…We proceeded to present the expression of univariate B-Spline basis function, which is defined through the following recurrence relationship [34]:…”

Section: Design Of the Feedfoward Term Based On Bsnnsmentioning

confidence: 99%

A New Adaptive RISE Feedforward Approach based on Associative Memory Neural Networks for the Control of PKMs

Escorcia-Hernández

Aguilar-Sierra

Aguilar-Mejía

et al. 2020

J Intell Robot Syst

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In this paper, a RISE (Robust Integral of the Sign Error) controller with adaptive feedforward compensation terms based on Associative Memory Neural Network (AMNN) type B-Spline is proposed to regulate the positioning of a Delta Parallel Robot (DPR) with three degrees of freedom. Parallel Kinematic Manipulators (PKMs) are highly nonlinear systems, so the design of a suitable control scheme represents a significant challenge given that these kinds of systems are continually dealing with parametric and non-parametric uncertainties and external disturbances. The main contribution of this work is the design of an adaptive feedforward compensation term using B-Spline Neural Networks (BSNNs). They make an on-line approximation of the DPR dynamics and integrates it into the control loop. The BSNNs' functions are bounded according to the extreme values of the desired joint space trajectories that are the BSNNs' inputs, and their weights are on-line adjusted by gradient descend rules. In order to evaluate the effectiveness of the proposed control scheme with respect to the standard RISE controller, numerical simulations for different case studies under different scenarios were performed.

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“…We proceeded to present the expression of univariate B-Spline basis function, which is defined through the following recurrence relationship [34]:…”

Section: Design Of the Feedfoward Term Based On Bsnnsmentioning

confidence: 99%

A New Adaptive RISE Feedforward Approach based on Associative Memory Neural Networks for the Control of PKMs

Escorcia-Hernández

Aguilar-Sierra

Aguilar-Mejía

et al. 2020

J Intell Robot Syst

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“…where a is a P -dimensional vector which contains the outputs of the base for P = 1, ..., 4 and, w is the weights vector. The B-Spline base function is defined in the following form [24]:…”

Section: Control Strategymentioning

confidence: 99%

An Intelligent Compensation Through B-Spline Neural Network for a Delta Parallel Robot

Escorcia-Hernández

Aguilar-Sierra

Aguilar-Mejía

et al. 2019

2019 6th International Conference on Control, Decision and Information Technologies (CoDIT)

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In this paper a PD controller with intelligent compensation is used to solve the problem of tracking trajectories for a Delta Parallel Robot with three degrees of freedom. This controller uses an artificial B-Spline neural network as a feedforward compensation term. To evaluate the proposed controller performance some numerical simulations under two different scenarios have been carried out in order to know its effectiveness respect to a simple PD controller.

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“…B-splines are basis functions for the spline function space [1], making them an attractive choice for approximating smooth continuous functions. For this reason, Bsplines have had numerous applications in system identification [2,3,4,5,6,7,8] and control [9,10,11,12]. The generalization of B-splines to multiple dimensions is done through tensor products of their univariate basis functions.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear system identification with regularized Tensor Network B-splines

Karagoz

Batselier

2020

Preprint

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This article introduces the Tensor Network B-spline model for the regularized identification of nonlinear systems using a nonlinear autoregressive exogenous (NARX) approach. Tensor network theory is used to alleviate the curse of dimensionality of multivariate B-splines by representing the high-dimensional weight tensor as a low-rank approximation. An iterative algorithm based on the alternating linear scheme is developed to directly estimate the low-rank tensor network approximation, removing the need to ever explicitly construct the exponentially large weight tensor. This reduces the computational and storage complexity significantly, allowing the identification of NARX systems with a large number of inputs and lags. The proposed algorithm is numerically stable, robust to noise, guaranteed to monotonically converge, and allows the straightforward incorporation of regularization. The TNBS-NARX model is validated through the identification of the cascaded watertank benchmark nonlinear system, on which it achieves state-of-the-art performance while identifying a 16-dimensional B-spline surface in 4 seconds on a standard desktop computer. An open-source MATLAB implementation is available on GitHub.

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Dynamic multivariate B-spline neural network design using orthogonal least squares algorithm for non-linear system identification

Cited by 6 publications

References 12 publications

A New Adaptive RISE Feedforward Approach based on Associative Memory Neural Networks for the Control of PKMs

A New Adaptive RISE Feedforward Approach based on Associative Memory Neural Networks for the Control of PKMs

An Intelligent Compensation Through B-Spline Neural Network for a Delta Parallel Robot

Nonlinear system identification with regularized Tensor Network B-splines

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