Improvements in stable inversion of NARX models by using Mann iteration

Eksteen, Johannes Jacobus Arnoldi; Heyns, P.S.

doi:10.1080/17415977.2015.1055262

Cited by 3 publications

(9 citation statements)

References 13 publications

(10 reference statements)

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“…These results do not represent an improvement on the results of stable inversion Eq. 79 for the same desired input and output signal in Example 3 of [13], for which we get lower input and output errors of 13.3% and 8.1% respectively. It is found that in all cases except when using no Q filter the best ILC results were obtained using iteration-dependent ILC gains.…”

Section: Example 3: Ilc Using An Approximate Linear Inverse Modelmentioning

confidence: 76%

“…Finally, we also note that the use of Mann [12] and Ishikawa iteration in stable inversion [13] has an analogy in ILC in that the conventional and alternative ILC algorithms developed here both have parallels in the Picard and Mann iteration schemes. It is furthermore shown that the application of Ishikawa iteration to ILC result in novel ILC iteration schemes for both the conventional and alternative ILC algorithms.…”

Section: Introductionmentioning

confidence: 95%

“…79 using the low-level random input and corresponding output signal of Example 2 in [13], shown in Fig. 7, to demonstrate the ability of the alternative ILC algorithm to converge when the conventional algorithm diverges in this particular case.…”

Section: Example 2: Ilc For a Random Desired Signalmentioning

confidence: 99%

“…79 using the higher-level random input and corresponding output signal of Example 3 in [13], shown in Fig. 10.…”

Section: Example 3: Ilc Using An Approximate Linear Inverse Modelmentioning

confidence: 99%

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An alternative update formula for non-linear model-based iterative learning control

Eksteen

Heyns

2015

Inverse Problems in Science and Engineering

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The conventional Iterative Learning Control (ILC) algorithm for model-based ILC of nonlinear systems is presented with use of a nonlinear inverse model as ILC compensator. The nonlinear inverse model is solved with stable inversion. In addition an alternative ILC algorithm for model-based ILC of nonlinear systems is developed, also with using a nonlinear inverse model as ILC compensator. Some connections between the conventional and alternative ILC algorithms and Picard, Mann and Ishikawa iteration are explored. In a number of theoretical examples the conventional and alternative algorithms are compared.

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Section: Example 3: Ilc Using An Approximate Linear Inverse Modelmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 95%

Section: Example 2: Ilc For a Random Desired Signalmentioning

confidence: 99%

“…79 using the higher-level random input and corresponding output signal of Example 3 in [13], shown in Fig. 10.…”

Section: Example 3: Ilc Using An Approximate Linear Inverse Modelmentioning

confidence: 99%

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An alternative update formula for non-linear model-based iterative learning control

Eksteen

Heyns

2015

Inverse Problems in Science and Engineering

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“…which enables the synthesis of the ILILC learning matrix (31). With this, the complete synthesis of ILILC with stable inversionstarting from a model in the normal form ( 12)-can be summarized by Procedure 1.…”

Section: Initial Picard Iteratẽ (0) Selection and Implementationmentioning

confidence: 99%

Iterative learning control with discrete‐time nonlinear nonminimum phase models via stable inversion

Spiegel

Strijbosch

Oomen

et al. 2021

Intl J Robust & Nonlinear

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Output reference tracking can be improved by iteratively learning from past data to inform the design of feedforward control inputs for subsequent tracking attempts. This process is called iterative learning control (ILC). This article develops a method to apply ILC to systems with nonlinear discrete-time dynamical models with unstable inverses (i.e. discrete-time nonlinear non-minimum phase models). This class of systems includes piezoactuators, electric power converters, and manipulators with flexible links, which may be found in nanopositioning stages, rolling mills, and robotic arms, respectively. As these devices may be required to execute fine transient reference tracking tasks repetitively in contexts such as manufacturing, they may benefit from ILC. Specifically, this article facilitates ILC of such systems by presenting a new ILC synthesis framework that allows combination of the principles of Newton's root finding algorithm with stable inversion, a technique for generating stable trajectories from unstable models. The new framework, called Invert-Linearize ILC (ILILC), is validated in simulation on a cart-and-pendulum system with model error, process noise, and measurement noise. Where preexisting Newton-based ILC diverges, ILILC with stable inversion converges, and does so in less than one third the number of trials necessary for the convergence of a gradient-descent-based ILC technique used as a benchmark.

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An iterative method and its application to stable inversion

et al. 2018

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In this paper, we study convergence and data dependence of SP and normal-S iterative methods for the class of almost contraction mappings under some mild conditions. The validity of these theoretical results is confirmed with numerical examples. It has been observed that a special case of SP iterative method, namely, normal-S iterative method, performs better and so the latter is implemented in the stable inversion of nonlinear discrete time dynamical systems to yield convergence results when Picard iterative method diverges. This is also illustrated with a numerical example. Our work extends and improves upon many results existing in the literature.

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Improvements in stable inversion of NARX models by using Mann iteration

Cited by 3 publications

References 13 publications

An alternative update formula for non-linear model-based iterative learning control

An alternative update formula for non-linear model-based iterative learning control

Iterative learning control with discrete‐time nonlinear nonminimum phase models via stable inversion

An iterative method and its application to stable inversion

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