Parameter estimation of nonlinearly parameterized regressions without overparameterization: Application to adaptive control

Gromov, Vladislav S.; Nuño, Emmanuel; Pyrkin, Anton A.; Romero, José Guadalupe

doi:10.1016/j.automatica.2021.109544

Cited by 25 publications

(50 citation statements)

References 26 publications

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“…Since we proved that Φ is bounded, to establish boundedness of ξ it suffices to prove that z is bounded. Towards this end, we replace (18) or (19) in the z dynamics of (6a) to get…”

mentioning

confidence: 99%

A new on-line exponential parameter estimator without persistent excitation

Korotina

Romero

Aranovskiy

et al. 2022

Systems & Control Letters

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“…Since we proved that Φ is bounded, to establish boundedness of ξ it suffices to prove that z is bounded. Towards this end, we replace (18) or (19) in the z dynamics of (6a) to get…”

mentioning

confidence: 99%

A new on-line exponential parameter estimator without persistent excitation

Korotina

Romero

Aranovskiy

et al. 2022

Systems & Control Letters

View full text Add to dashboard Cite

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“…In contrast with this approach we consider here the case where the uncertain parameters enter into the system dynamics in a nonlinear way and construct a nonlinearly parameterized regression equation (NLPRE). The interested reader is referred to 14,7 for recent reviews of the literature dealing with NLPRE.…”

Section: C1mentioning

confidence: 99%

“…In contrast to the results in 7,12 where, to prove parameter convergence, it is necessary to assume some a priori non-verifiable conditions, in this paper we use the parameter estimator proposed in 15 -called G+D estimator-that ensures (global exponential) parameter convergence assuming only the extremely weak condition of interval excitation 16,17 of the original vector regressor. An additional advantage of the G+D estimator is that it can deal with a class of NLPREs-in particular, separable ones.…”

Section: C2mentioning

confidence: 99%

“…This is a significant simplification that drastically reduces the complexity and computational demands. To the best of our knowledge, such an approach was never actually pursued, because the excitation requirements for the consistent estimation of the parameters is "very high"-see 7,Remark 16 . In the recent paper 12 a procedure to overcome, for the first time, this fundamental problem was proposed.…”

Section: Introductionmentioning

confidence: 99%

“…The main contributions of the paper, which include several generalizations of the results in 7,12 , may be summarized as follows.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Indirect Adaptive Control of Nonlinearly Parameterized Nonlinear Dissipative Systems

Cisneros¹,

Wang²,

Schaft³

2022

Preprint

Self Cite

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In this note we address the problem of indirect adaptive (regulation or tracking) control of nonlinear, input affine dissipative systems. It is assumed that the supply rate, the storage and the internal dissipation functions may be expressed as nonlinearly parameterized regression equations where the mappings (depending on the unknown parameters) satisfy a monotonicity condition-this encompasses a large class of physical systems, including passive systems. We propose to estimate the system parameters using the "power-balance" equation, which is the differential version of the classical dissipation inequality, with a new estimator that ensures global, exponential, parameter convergence under the very weak assumption of interval excitation of the power-balance equation regressor. To design the indirect adaptive controller we make the standard assumption of existence of an asymptotically stabilizing controller that depends-possibly nonlinearly-on the unknown plant parameters, and apply a certainty-equivalent control law. The benefits of the proposed approach, with respect to other existing solutions, are illustrated with examples.

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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.

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Parameter estimation of nonlinearly parameterized regressions without overparameterization: Application to adaptive control

Cited by 25 publications

References 26 publications

A new on-line exponential parameter estimator without persistent excitation

A new on-line exponential parameter estimator without persistent excitation

Indirect Adaptive Control of Nonlinearly Parameterized Nonlinear Dissipative Systems

Unknown piecewise constant parameters identification with exponential rate of convergence

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