Parameter Estimation of Nonlinearly Parameterized Regressions: Application to System Identification and Adaptive Control

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

doi:10.1016/j.ifacol.2020.12.1439

Cited by 13 publications

(15 citation statements)

References 9 publications

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“…where S : R q → R p , with p ≥ q is a known mapping of the vector of unknown parameters θ. Similarly to [9], [40], [55] the property that we exploit to achieve the estimation objective is monotonicity, which is defined with the following non-standard assumption.…”

Section: Nonlinearly Parameterized Regression Equationsmentioning

confidence: 99%

Identifiability Implies Robust, Globally Exponentially Convergent On-line Parameter Estimation: Application to Model Reference Adaptive Control

Wang,

Ortega,

Bobtsov

et al. 2021

Preprint

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In this paper we propose a new parameter estimator that ensures global exponential convergence of linear regression models requiring only the necessary assumption of identifiability of the regression equation, which we show is equivalent to interval excitation of the regressor vector. Continuous and discrete-time versions of the estimators are given. An extension to-separable and monotonic-non-linear parameterizations is also given. The estimators are shown to be robust to additive measurement noise and-not necessarily slow-parameter variations. Moreover, a version of the continuous-time estimator that rejects sinusoidal disturbances with unknown internal model is given. The estimator is shown to be applicable to the classical model reference adaptive control problem relaxing the conspicuous assumption of known sign of the high-frequency gain. Simulation results that illustrate the performance of the estimator are given.

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Section: Nonlinearly Parameterized Regression Equationsmentioning

confidence: 99%

Identifiability Implies Robust, Globally Exponentially Convergent On-line Parameter Estimation: Application to Model Reference Adaptive Control

Wang,

Ortega,

Bobtsov

et al. 2021

Preprint

Self Cite

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“…The application of our result to discrete-time systems follows verbatim the one given here. The interested reader is referred to [13] where such an algorithm is presented for the more challenging problem of nonlinearly parameterized, separable regressions, that is, when y = ΨΦ(θ), with Φ(•) a nonlinear mapping. E4.…”

Section: Further Extensions and Discussionmentioning

confidence: 99%

Distributed Observers for LTI Systems with Finite Convergence Time: A Parameter Estimation-based Approach

Nuño¹,

Bobtsov²

2020

Preprint

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A novel approach to solve the problem of distributed state estimation of linear time-invariant systems is proposed in this paper. It relies on the application of parameter estimation-based observers, where the state observation task is reformulated as a parameter estimation problem. In contrast with existing results our solution achieves convergence in finite-time, without injection of high gain, and imposes very weak assumptions on the communication graphnamely the existence of a Hamiltonian walk. The scheme is shown to be robust vis-á-vis external disturbances and communication delays.

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“…Indeed, it consists of the sum of a "classical" linear regression equation (LRE) with all the unknown constant parameters and a term which depends nolinearly on these parameters. As it has been shown in [18], thanks to the use of the DREM technique-that generates scalar LREs for separable nonlinearly parameterized regressions-it is possible to use for the parameter estimation only the first, linear part of the regression equation and disregard the nonlinear part of it.…”

Section: Reducing the Observation Problem To Estimation Of Parametersmentioning

confidence: 99%

An Adaptive Observer for Uncertain Linear Time-Varying Systems with Unknown Additive Perturbations

Pyrkin¹,

Bobtsov²,

Romeo³

et al. 2021

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In this paper we are interested in the problem of adaptive state observation of linear timevarying (LTV) systems where the system and the input matrices depend on unknown timevarying parameters. It is assumed that these parameters satisfy some known LTV dynamics, but with unknown initial conditions. Moreover, the state equation is perturbed by an additive signal generated from an exosystem with uncertain constant parameters. Our main contribution is to propose a globally convergent state observer that requires only a weak excitation assumption on the system.

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Parameter Estimation of Nonlinearly Parameterized Regressions: Application to System Identification and Adaptive Control

Cited by 13 publications

References 9 publications

Identifiability Implies Robust, Globally Exponentially Convergent On-line Parameter Estimation: Application to Model Reference Adaptive Control

Identifiability Implies Robust, Globally Exponentially Convergent On-line Parameter Estimation: Application to Model Reference Adaptive Control

Distributed Observers for LTI Systems with Finite Convergence Time: A Parameter Estimation-based Approach

An Adaptive Observer for Uncertain Linear Time-Varying Systems with Unknown Additive Perturbations

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