Identification of multiple local nonlinear attachments using a single measurement case

Singh, Aryan; Moore, Kate

doi:10.1016/j.jsv.2021.116410

“…The second nonlinearity approximates by a time series. In [11], the method presented to design mathematical models for the dynamic system on a set of local nonlinear attachments. Devices installed in the same primary construction.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Parametric Identification of Systems with Multiple Nonlinearities

Karabutov¹

2023

Preprint

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The system identification problem with multiple nonlinearities is relevant. Its decision depends on many factors. These include: feedbacks, the method of connecting nonlinear links, signal properties. They affect the identifiability of the system parameters. We introduced a condition for the excitation constancy for state variables, which considers the S-identifiability of the system. We propose system decomposition by measuring input to identify parameters. Each subsystem has an implicit identification representation. It guarantees obtaining estimates of subsystem parameters based on experimental data. The trajectories boundedness of adaptive system proved in parametric and coordinate spaces. Conditions guaranteeing exponential stability of the system obtained. Systems of self-oscillation generation and nonlinear correction of a nonlinear system consider. Conditions for the trajectories boundedness of the adaptive system obtained for these cases. The influence of nonlinearity and feedback on the system performance estimated.

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“…2 of 25 nonlinearity approximates by a time series. In [11], the method presented to design mathematical models for the dynamic system on a set of local nonlinear attachments. Devices installed in the same primary construction.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Parametric Identification of Systems with Multiple Nonlinearities

Karabutov¹

2023

Preprint

0

View full text Add to dashboard Cite

The system identification problem with multiple nonlinearities is relevant. Its decision depends on many factors. These include: feedbacks, the method of connecting nonlinear links, signal properties. They affect the identifiability of the system parameters. We introduced a condition for the excitation constancy for state variables, which considers the S-identifiability of the system. We propose system decomposition by measuring input to identify parameters. Each subsystem has an implicit identification representation. It guarantees obtaining estimates of subsystem parameters based on experimental data. The trajectories boundedness of adaptive system proved in parametric and coordinate spaces. Conditions guaranteeing exponential stability of the system obtained. Systems of self-oscillation generation and nonlinear correction of a nonlinear system consider. Conditions for the trajectories boundedness of the adaptive system obtained for these cases. The influence of nonlinearity and feedback on the system performance estimated.

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“…Идентификации систем с несколькими нелинейностями (СНН) посвящен ряд исследований [1][2][3][4][5][6][7][8][9][10][11]. В [1] рассмотрен случай, когда система содержит несколько последовательно включенных нелинейностей и предложен способ идентификации.…”

Section: Introductionunclassified

“…Модель имеет вид «серого ящика» и основана на применении нелинейных базисных функций с использованием ограниченного числа измеренных выходных переменных. Другие подходы к идентификации рассмотрены в [10][11][12][13][14]. Они основаны на учете физических законов при выборе структуры модели [11], применении частотных методов для системы с обратной связью [12] и теории обучения [13].…”

Section: Introductionunclassified

On adaptive identification of systems having multiple nonlinearities

Karabutov

2023

Rossijskij tehnologičeskij žurnal

2

0

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Objectives. The solution to the relevant problem of identifying systems with multiple nonlinearities depends on such factors as feedback, ways of connecting nonlinear links, and signal properties. The specifics of nonlinear systems affect control systems design methods. As a rule, the basis for the development of a mathematical model involves the linearization of a system. Under conditions of uncertainty, the identification problem becomes even more relevant. Therefore, the present work sets out to develop an approach to the identification of nonlinear dynamical systems under conditions of uncertainty. In order to obtain a solution to the problem, an adaptive identification method is developed by decomposing the system into subsystems.Methods. Methods applied include the adaptive identification method, implicit identified representation, S-synchronization of a nonlinear system, and the Lyapunov vector function method.Results. A generalization of the excitation constancy condition based on fulfilling the S-synchronizability for a nonlinear system is proposed along with a method for decomposing the system in the output space. Adaptive algorithms are obtained on the basis of the second Lyapunov method. The boundedness of the adaptive system trajectories in parametric and coordinate spaces is demonstrated. Approaches for self-oscillation generation and nonlinear correction of a nonlinear system are considered along with obtained exponential stability conditions for the adaptive system.Conclusions. Simulation results confirm the possibility of applying the proposed approach to solving the problems of adaptive identification while taking the estimation of the structural identifiability (S-synchronization) of the system nonlinear part into account. The influence of the structure and relations of the system on the quality of the obtained parametric estimates is investigated. The proposed methods can be used in developing identification and control systems for complex dynamic systems.

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Identification of multiple local nonlinear attachments using a single measurement case

Cited by 13 publications

References 32 publications

Adaptive Parametric Identification of Systems with Multiple Nonlinearities

Adaptive Parametric Identification of Systems with Multiple Nonlinearities

Adaptive Parametric Identification of Systems with Multiple Nonlinearities

On adaptive identification of systems having multiple nonlinearities

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