Flux Observer for the Levitated Ball with Relaxed Excitation Conditions

Ovcharov, Alexey; Vedyakov, Alexey A.; Sviatoslav, Kazak; Bespalov, Vladimir; Pyrkin, Anton A.; Bobtsov, Alexey A.

doi:10.23919/ecc54610.2021.9654955

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…Figure 8 shows the comparison of a) + and the estimate ̂ + , b) ‖ ‖ ̃ ( ) ‖ ‖ and its asymptotic upper bound (UB), which was calculated using (26).…”

Section: Simple Noised Scenariomentioning

confidence: 99%

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Glushchenko¹,

Lastochkin²

2022

Preprint

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The scope of this research is the identification of piecewise constant parameters of linear regression equations under the finite excitation condition. Such an equation is considered as a switched system, which identification usually consists of three main steps: a switching time instant detection, choice of the most appropriate model from the known set or generation of a new one, online adjustment of the chosen model parameters. Compared to the known methods, to make the computational burden lower and simplify the stability analysis, we use only one model to identify all switching states of the regression. So, the proposed identification procedure includes only two main approaches. The first one is a new estimation algorithm to detect switching time and preserve time alertness, which is based on a well-known DREM procedure and ensures adjustable detection delay. Unlike existing solutions, it does not involve an offline operation of data monitoring and stacking. The second one is the adaptive law, which provides element-wise monotonous exponential convergence of the regression parameters to their true values over the time range between two consecutive switches. Its convergence condition is that the regressor is finitely exciting somewhere inside such time interval. The robustness of the proposed identification procedure to the influence of external disturbances is analytically proved.Its effectiveness is demonstrated via numerical experiments, in which both abstract regressions and a second-order plant model are used.

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“…Figure 8 shows the comparison of a) + and the estimate ̂ + , b) ‖ ‖ ̃ ( ) ‖ ‖ and its asymptotic upper bound (UB), which was calculated using (26).…”

Section: Simple Noised Scenariomentioning

confidence: 99%

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Glushchenko¹,

Lastochkin²

2022

Preprint

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“…На сегодняшний день в известной авторам литературе предложено два основных подхода [12][13][14], ослабляющих условие реализуемости базовой процедуры DREM до требования частичного конечного возбуждения.…”

Section: Introductionunclassified

“…Во втором случае этот подход обеспечивает качество идентификации неизвестных параметров, соответствующее стандартному градиентному идентификатору, что и является его основным недостатком. В [13,14] на основе модифицированного процесса Грамма-Шмидта предложен и развит алгоритм удаления линейно зависимых строк и столбцов из матрицы расширенного регрессора, позволяющий при известной аналитической зависимости неизвестных параметров привести задачу идентификации неизвестных параметров к задаче численного решения систем алгебраических уравнений. Однако вызывает определенные сомнения возможность решения данных уравнений для независимых неизвестных параметров и, следовательно, расширения на общий случай результата, полученного в [13,14].…”

Section: Introductionunclassified

Ослабление Условия Реализуемости Процедуры Динамического Расширения И Смешивания

2023

Автомат. и телемех.

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Предлагается обобщение процедуры динамического расширения и смешивания, которое в отличие от базовой процедуры, во-первых, гарантирует убывание ошибки идентификации неизвестных параметров при выполнении условия частичного конечного возбуждения регрессора, а во-вторых, при частичном неисчезающем возбуждении регрессора с рангом не менее единицы обеспечивает экспоненциальную сходимость к нулю ошибки слежения за регрессионной функцией.

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Unknown piecewise constant parameters identification with exponential rate of convergence

Glushchenko

Lastochkin

2022

Adaptive Control & Signal

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Summary The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one model to identify all switching states of the regression is used in the developed procedure with the following two‐fold contribution. First of all, we propose a new truly online estimation algorithm based on a well‐known DREM approach to detect switching time and preserve time alertness with adjustable detection delay. Second, despite the fact that a switching signal function is unknown, the adaptive law is derived that provides global exponential convergence of the regression parameters estimates to their true values in case the regressor is finitely exciting somewhere inside the time interval between two consecutive parameters switches. The robustness of the proposed identification procedure to the influence of external disturbances is analytically proved. Its effectiveness is demonstrated via numerical experiments, in which both abstract regressions and a second‐order plant model are used.

show abstract

Flux Observer for the Levitated Ball with Relaxed Excitation Conditions

Cited by 4 publications

References 14 publications

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Ослабление Условия Реализуемости Процедуры Динамического Расширения И Смешивания

Unknown piecewise constant parameters identification with exponential rate of convergence

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