Parameter Estimation in Systems with Time Delay and Closed Loop Systems

Kaminskas, Vytautas

doi:10.1016/s1474-6670(17)65478-8

Cited by 5 publications

(10 citation statements)

References 3 publications

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“…Then, the estimate

\overset{τ}{true} false(k false)

obtained by the local optimization technique, will get stuck on the nearest local minimum. Note that any multiextremal error function (see Figures A to C) turns round into the unimodal one (Figures D to F) if corrective filter followed by exponential one , is implemented into the recursive schema …”

Section: Simulation Resultsmentioning

confidence: 99%

“…There is a considerable amount of references available on parametric identification of dynamical systems with time delay, mentioned here just a few ones . Some of them can be used online for joint tracking of the current values of unknown varying in time coefficients and time delay by processing discrete‐time input‐output observations . For an unbiased parametric estimation of linear time invariant (LTI) systems in the case of an additive noise, a variety of adaptive methods and their algorithms is proposed .…”

Section: Introductionmentioning

confidence: 99%

“…Seeking the global extremum, it is needed, in each recursion, to use the filtering of signals by the so‐called corrective operator. It is used to transform available signals into the equivalent ones with a unimodal cross‐correlation function, in respect of the time delay . Afterwards, the initial criterion modifies its current form, turning out into the convex one.…”

Section: Introductionmentioning

confidence: 99%

“…Such a technique for Wiener systems is given here. The adaptive approach, based on the method of corrective operators, is not applied elsewhere, except in the works of Kaminskas and Pupeikis, where it is used for LTI input delayed systems. Here, this approach is developed for the Wiener systems quite successfully.…”

Section: Introductionmentioning

confidence: 99%

“…[3][4][5][6][7][8][9][10][11][12][13][14][15] Some of them can be used online for joint tracking of the current values of unknown varying in time coefficients and time delay by processing discrete-time input-output observations. 3,5,7,8,10,13,15 For an unbiased parametric estimation of linear time invariant (LTI) systems in the case of an additive noise, a variety of adaptive methods and their algorithms is proposed. 1,2,[16][17][18] In such a case, the presence of time delay has also to be taken into account.…”

Section: Introductionmentioning

confidence: 99%

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Tracking coefficients of a nonstationary system, followed by static nonlinearity jointly with the time delay

Pupeikis

2020

Adaptive Control & Signal

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Summary This paper considers a block‐oriented nonlinear Wiener system that consists of a linear block with real time‐varying unknown coefficients and pure time delay followed by a static invertible nonlinearity. Consideration is concentrated on the joint linear block coefficients and time delay tracking by processing observation samples. Two problems are analyzed. The first one is the avoidance of mean‐squares prediction error function multiextremality for time delay while seeking the global minimum. The other problem consists of the applicability of unified adaptive algorithms, based on the schema with corrective operators for the Wiener system. An approach used to transform the multiextremal criterion into a unimodal function for a nonstationary linear system, in respect of the time delay, is developed and analyzed for a block‐oriented nonlinear Wiener system with time‐varying coefficients and a time delay. The recursive parametric identification approach, based on the method of corrective operators, is developed for the nonstationary dynamic Wiener system. Applicability of algorithms is supported by various simulation tests solved by a computer.

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“…Then, the estimate

\overset{τ}{true} false(k false)

Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tracking coefficients of a nonstationary system, followed by static nonlinearity jointly with the time delay

Pupeikis

2020

Adaptive Control & Signal

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Joint tracking coefficients and the time delay of a nonstationary linear system, preceded by a static nonlinearity

Pupeikis

2021

Adaptive Control & Signal

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Summary The paper considers a block‐oriented nonlinear Hammerstein system that consists of a linear block with real‐valued time‐varying unknown coefficients and a pure time delay, preceded by the static nonlinearity. The joint tracking of linear block coefficients and the time delay while processing observation samples is under consideration. The difficulty of the tracking process consists in the initial nonconvexity of the objective function to be minimized, in respect of the time delay. To obtain current estimates of the true coefficients and the time delay it is necessary to overcome the multiextremality of the objective function. A global optimization problem could be solved by changing a form of the nonconvex objective function into a convex one. The optimization problem has been subdivided into two problems that are analyzed in this article, as well. The first one consists of removal of the objective function multiextremality in respect of the time delay, while hunting for the global extremum. Therefore, the well‐known approach based on the method of corrective operators, which is used to transform the multiextremal criterion into a unimodal function for the nonstationary Wiener system, is developed here for the Hammerstein one. The other problem consists of the applicability of unified adaptive algorithms, used for Wiener systems in the case of Hammerstein systems. The recursive parametric identification technique, based on the adaptive algorithm procedures, is developed here for the nonstationary block‐oriented Hammerstein systems, too. The applicability of algorithms is supported by various simulation tests solved by computer for distinct inputs and for two static nonlinearities.

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Useful redundancy in parameter and time delay estimation for continuous-time models

Welsh

Alamir

2018

Automatica

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This paper proposes an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with the estimation of a time delay system, we utilise the useful redundancy technique. Specifically, the cost function is filtered through a set of low-pass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.

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Parameter Estimation in Systems with Time Delay and Closed Loop Systems

Cited by 5 publications

References 3 publications

Tracking coefficients of a nonstationary system, followed by static nonlinearity jointly with the time delay

Tracking coefficients of a nonstationary system, followed by static nonlinearity jointly with the time delay

Joint tracking coefficients and the time delay of a nonstationary linear system, preceded by a static nonlinearity

Useful redundancy in parameter and time delay estimation for continuous-time models

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