Rapid identification of linear and nonlinear systems.

Lion, P. M.

doi:10.2514/3.4313

Cited by 163 publications

(69 citation statements)

References 4 publications

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“…It is included partially for purposes of self containment of the paper but we also require a more exact treatment, especially in regard to the effects of initial conditions, and transient terms. For more motivation and detail see [1]. Next,choose any constant k > 0, and define the a…”

Section: Lion's Identification Schemementioning

confidence: 99%

“…Consider the scalar, asymptotic^llly stable, reduced form, input-output representation (1) ( dn n + nFla i dl l )v( t ) -(…”

Section: Introductionmentioning

confidence: 99%

“…Mor-^ precisely, there is a least dimension, s.symptotically stable, systera In an interesting paper [1], Lion investigated a versatile method for id^^ntifyi n^; the ecnstant coefficients {ai ,b i } . In a.…”

Section: Introductionmentioning

confidence: 99%

“…The latter theoreu^ required periodicity. From the results of [1], one cannot assert convergence of the algorithm when zhe inputs are random. In this paper, an invariant set theorem for random systems [2] is applied to yield that Lion's algorithm converges for a very wide class of asymptotically stationary inputs.…”

Section: Introductionmentioning

confidence: 99%

“…stationary. An invariant set thecrem for random systems [2] is used to prove convergence (ir probability) of the identification algorithm proposed n [1].…”

mentioning

confidence: 99%

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On the convergence of Lion's identification method with random inputs

Kushner

1970

IEEE Trans. Automat. Contr.

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Section: Lion's Identification Schemementioning

confidence: 99%

“…Consider the scalar, asymptotic^llly stable, reduced form, input-output representation (1) ( dn n + nFla i dl l )v( t ) -(…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…stationary. An invariant set thecrem for random systems [2] is used to prove convergence (ir probability) of the identification algorithm proposed n [1].…”

mentioning

confidence: 99%

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On the convergence of Lion's identification method with random inputs

Kushner

1970

IEEE Trans. Automat. Contr.

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Algorithms of adaptive tracking of unknown multisinusoidal signals in linear systems with arbitrary input delay

Miliushin

Nikiforov

2019

Adaptive Control & Signal

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The problem of adaptive tracking control is addressed for the class of linear time-invariant plants with known parameters and arbitrary known input delay.The reference signal is a priori unknown and is represented by a sum of biased harmonics with unknown amplitudes, frequencies, and phases. Asymptotic tracking is provided by predictive adjustable control with parameters generated by one of three designed adaptation algorithms. The first algorithm is based on a gradient scheme and ensures zero steady-state tracking error with all signals bounded. The other two algorithms additionally involve the scheme with fast parametric convergence improving the closed-loop system performance. In all the algorithms, the problem of delay compensation is resolved by special augmentation of tracking error. The adjustable control law proposed do not require identification of the reference signal parameters. KEYWORDSadaptive tracking control, delayed systems, internal model principle 900

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Robust method to provide exponential convergence of model parameters solving linear time‐invariant plant identification problem

Glushchenko¹,

Petrov²,

Lastochkin³

2021

Adaptive Control & Signal

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Summary The scope of this research is a problem of parameters identification of a linear time‐invariant plant, which (1) input signal is not frequency‐rich, (2) is subjected to initial conditions and external disturbances. The memory regressor extension (MRE) scheme, in which a specially derived differential equation is used as a filter, is applied to solve the above‐stated problem. Such a filter allows us to obtain a bounded regressor value, for which a condition of the initial excitation (IE) is met. Using the MRE scheme, the recursive least‐squares method with the forgetting factor is used to derive an adaptation law. The following properties have been proved for the proposed approach. If the IE condition is met, then: (1) the parameter error of identification is bounded and converges to zero exponentially (if there are no external disturbances) or to a set (in the case of them) with an adjustable rate, (2) the parameters adaptation rate is a finite value. The above‐mentioned properties are mathematically proved and demonstrated via simulation experiments.

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Rapid identification of linear and nonlinear systems.

Cited by 163 publications

References 4 publications

On the convergence of Lion's identification method with random inputs

On the convergence of Lion's identification method with random inputs

Algorithms of adaptive tracking of unknown multisinusoidal signals in linear systems with arbitrary input delay

Robust method to provide exponential convergence of model parameters solving linear time‐invariant plant identification problem

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