2008
DOI: 10.1007/978-1-84800-161-9_13
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Closed-loop Parametric Identification for Continuous-time Linear Systems via New Algebraic Techniques

Abstract: Summary. Closed-loop parametric identification of continuous-time linear systems is achieved via new algebraic techniques, which are employing non-commutative ring theory, module theory, and operational calculus. The efficiency and robustness with respect to noises are demonstrated by three illustrative examples and their computer simulations. In two of them we compare our results with those given by standard adaptive methods.

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Cited by 150 publications
(140 citation statements)
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“…Estimation of F F in Equation (1) is assumed to be "well" approximated by a piecewise constant function F est . According to the algebraic parameter identification developed in [12], [13], rewrite, if ν = 1 for simplicity's sake, Equation (5) in the operational domain (see [31] for instance) sY = Φ s + αU + y(0) where Φ is a constant. We get rid of the initial condition y(0) by multiplying both sides on the left by d ds :…”
Section: B Intelligent Pidsmentioning
confidence: 99%
“…Estimation of F F in Equation (1) is assumed to be "well" approximated by a piecewise constant function F est . According to the algebraic parameter identification developed in [12], [13], rewrite, if ν = 1 for simplicity's sake, Equation (5) in the operational domain (see [31] for instance) sY = Φ s + αU + y(0) where Φ is a constant. We get rid of the initial condition y(0) by multiplying both sides on the left by d ds :…”
Section: B Intelligent Pidsmentioning
confidence: 99%
“…According to the algebraic parameter identification developed in [9], [10], rewrite, if ν = 1, Equation (2) in the operational domain (see, e.g., [26])…”
Section: Model-free Control: a Short Reviewmentioning
confidence: 99%
“…Another fractional integration by parts formula has also been given in [18], however the Caputo fractional derivative was involved in the formula; on the other hand, the initial conditions of the fractional derivatives of y can be eliminated using a modulating function. In fact, the idea of obtaining this theorem is inspired by the recent algebraic parametric estimation technique [19], [20], [21], [22], [23], [24], [25], [26], which eliminates the unknown initial conditions by applying algebraic manipulations in the frequency domain.…”
Section: Fractional Integration By Partsmentioning
confidence: 99%