Publication

Iterative Learning Control Using Stochastic Approximation Theory with Application to a Mechatronic System

2010
Book Chapters

Abstract

In this paper it is shown how Stochastic Approximation theory can be used to derive and analyse well-known Iterative Learning Control algorithms for linear systems. The Stochastic Approximation theory gives conditions that, when satisfied, ensure almost sure convergence of the algorithms to the optimal input in the presence of stochastic disturbances. The practical issues of monotonic convergence and robustness to model uncertainty are considered. Specific choices of the learning matrix are studied, as well as a model-free choice. Moreover, the model-free method is applied to a linear motor system, leading to greatly improved tracking.

Official source

https://infoscience.epfl.ch/entities/publication/a70834dc-f352-45de-9e98-a50ad9e0e16d

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2010
Book Chapters

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a70834dc-f352-45de-9e98-a50ad9e0e16d

About this result

Related concepts (32)

Learning rate

In machine learning and statistics, the learning rate is a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function. Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a machine learning model "learns". In the adaptive control literature, the learning rate is commonly referred to as gain. In setting a learning rate, there is a trade-off between the rate of convergence and overshooting.

Convergence tests

In mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series . If the limit of the summand is undefined or nonzero, that is , then the series must diverge. In this sense, the partial sums are Cauchy only if this limit exists and is equal to zero. The test is inconclusive if the limit of the summand is zero. This is also known as the nth-term test, test for divergence, or the divergence test.

Integral test for convergence

In mathematics, the integral test for convergence is a method used to test infinite series of monotonous terms for convergence. It was developed by Colin Maclaurin and Augustin-Louis Cauchy and is sometimes known as the Maclaurin–Cauchy test. Consider an integer N and a function f defined on the unbounded interval , on which it is monotone decreasing. Then the infinite series converges to a real number if and only if the improper integral is finite. In particular, if the integral diverges, then the series diverges as well.

Related publications (3)

Iterative Learning Control Using Stochastic Approximation Theory with Application to a Mechatronic System

Chat with Graph Search

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