Adaptive Estimation of Time-Varying Parameters in Linearly Parametrized Systems

Zhu, Ye; Pagilla, Prabhakar R.

doi:10.1115/1.2234488

Cited by 23 publications

(41 citation statements)

References 9 publications

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“…In general, exponential convergence in the constant parameter case, guarantees some degree of tracking for a sufficiently slowly-varying signal [21], [22]. The topic of time-varying parameters has been the focus of several studies [23], [24], [25], [26]. In DIVE mode identification using AFM [19], the viscoelastic properties of the sample are considered spatially inhomogeneous but constant in time.…”

Section: Introductionmentioning

confidence: 99%

Exponential convergence bounds in least squares estimation: Identification of viscoelastic properties in atomic force microscopy

Ragazzon

Gravdahl

Pettersen

2017

2017 IEEE Conference on Control Technology and Applications (CCTA)

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Abstract-Using atomic force microscopy (AFM) for studying soft, biological material has become increasingly popular in recent years. New approaches allow the use of recursive least squares estimation to identify the viscoelastic properties of a sample in AFM. As long as the regressor vector is persistently exciting (PE), exponential convergence of the parameters to be identified can be guaranteed. However, even exponential convergence can be slow. In this article, upper bounds on the parameter convergence is found, completely determined by the PE properties and least squares update law parameters. Furthermore, for a parameter vector which is piecewise constant at regular intervals, the time interval necessary for the error to converge to any specified upper limit is determined. For a soft sample in AFM, the viscoelastic properties can be spatially inhomogeneous. These properties can be spatially resolved by periodically tapping at discrete points along the sample. The results of this article then allows us to determine the time interval necessary at each tap in order to guarantee convergence to any specified fraction of the step-change in the parameters. Simulation results are presented, demonstrating the applicability of the approach.

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Section: Introductionmentioning

confidence: 99%

Exponential convergence bounds in least squares estimation: Identification of viscoelastic properties in atomic force microscopy

Ragazzon

Gravdahl

Pettersen

2017

2017 IEEE Conference on Control Technology and Applications (CCTA)

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“…Consequently, the idea of [20] by using the parameter estimation error to design the adaptive laws can be employed, and then fast error convergence and the robustness to the bounded disturbances are all achieved without using the predictor design. To guarantee the continuity of the estimation for all time, a parameter resetting scheme [13] will be introduced. Finally, we prove that the estimation error converges to a neighborhood around zero in FT, where the size depends on the excitation level and the upper bounds of disturbances.…”

Section: Introductionmentioning

confidence: 99%

“…It is noted that such approximations are valid within finite-time (FT) interval and thus, an initial condition resetting scheme should be investigated to guarantee the continuity of the estimated parameters. Moreover, the disturbances and the potential approximation errors are not considered in [13]. Following this framework, the authors of [14] proposed an alternative polynomial approximation-based estimation, where the direct LS scheme is used to estimate the coefficients of the employed polynomials.…”

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confidence: 99%

“…This condition may be stringent in practice. In the latest work [7], an updating scheme for the parameter uncertainty set is incorporated into the projection-based adaptive laws so that the guaranteed bounds for the uncertainty of the parameter estimates can be retained.On the other hand, it is noted that most of the aforementioned results depend on an extra predictor or observer design, where the induced predictor/observer errors are used to drive the adaptations for estimating unknown parameters [10][11][12][13]. Within this framework, a large adaptive gain should be used to achieve fast adaptation, which may result in high-frequency oscillations when the system subjects to a large source of uncertainties or disturbances [3].…”

mentioning

confidence: 99%

“…On the other hand, it is noted that most of the aforementioned results depend on an extra predictor or observer design, where the induced predictor/observer errors are used to drive the adaptations for estimating unknown parameters [10][11][12][13]. Within this framework, a large adaptive gain should be used to achieve fast adaptation, which may result in high-frequency oscillations when the system subjects to a large source of uncertainties or disturbances [3].…”

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confidence: 99%

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Robust adaptive estimation of nonlinear system with time‐varying parameters

Yang

Ren

et al. 2014

Adaptive Control & Signal

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The vast majority of available parameter estimation methods assume that the parameters to be estimated are constant or slowly time-varying and mainly depend on a predictor or observer design so that a large adaptive gain must be used to achieve fast adaptation; this may result in high-frequency oscillations when the system subjects to a large source of uncertainties or disturbances. This paper is concerned with adaptive online estimation of time-varying parameters for two kinds of linearly parameterized nonlinear systems. By dividing the time into small intervals, the time-varying parameters are approximated in terms of polynomials with unknown coefficients. Then a novel adaptive law design methodology is developed to estimate those constant coefficients, for which the parameter estimation error information is explicitly derived and used to drive the adaptations. To guarantee the continuity of the parameter estimation for all time, a parameter resetting scheme is introduced at the beginning of each interval. Finite-time estimation convergence and the robustness against disturbances are all proved. Extensive simulation examples are provided to demonstrate the efficacy of the proposed algorithms for estimating time-varying parameters.In practical systems, time-varying behavior of the plant parameters may be unavoidable due to the complex mechanisms, the model-plant mismatch, or unmeasured inputs that affect the system dynamics [7,8]. Consequently, the estimation of such time-varying behaviors is of great importance for the control system design. To address this issue, some efforts have been advanced to exploit the ability of gradient algorithms and LS algorithms to estimate time-varying parameters. In particular, various well-known approaches, for example, gradient, recursive/nonrecursive LS algorithms and modified LS algorithms with constant/variable forgetting factor, are reviewed and compared in terms of performance and robustness [9]. It is shown in [9] that the nonrecursive algorithms are more robust to disturbances under slowly time-varying parameters. In [10], the application of a local regression of a time-related polynomial for the RLS algorithm with a forgetting factor is validated to reduce the mean-square estimation error. However, these algorithms all assume that the parameters to be estimated are slowly time-varying, that is, they may fail to retain their properties for fast time-varying parameters.It is well-known that a continuous time-varying function can be locally approximated by polynomials with constant coefficients. Following this idea, with the assumption that the time-varying parameters can be precisely represented as a linear combination of known functions and unknown constants [11,12], conventional LS estimation has been adopted for time-varying systems. In [13], a local Taylor expansion of a time-related polynomial is used to approximate time-varying parameters, and the induced constant Taylor series coefficients are estimated by using standard LS approach. It is noted that such approxima...

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On‐line parameter estimation for a class of time‐varying continuous systems with bounded disturbances

Chen¹,

Zhang²,

Li³

2010

Adaptive Control & Signal

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In this paper, we proposed an on-line parameter estimation algorithm for a class of time-varying continuous systems with bounded disturbance. In this method, a novel polynomial approximator with a bounded regressor vector is constructed and utilized to approximate the time-varying parameters. The direct leastsquares algorithm is employed to acquire the on-line estimates, so that several useful properties of the direct estimation, such as fast convergence and robustness to the bounded disturbance, are reflected in our method. We have proved that the estimation error of this method is bounded. Furthermore, the bound on the Euclidean norm of the estimation error is derived. The simulation results demonstrate that this method can provide accurate estimates of time-varying parameters even under the influence of bounded disturbance.

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Adaptive Estimation of Time-Varying Parameters in Linearly Parametrized Systems

Cited by 23 publications

References 9 publications

Exponential convergence bounds in least squares estimation: Identification of viscoelastic properties in atomic force microscopy

Exponential convergence bounds in least squares estimation: Identification of viscoelastic properties in atomic force microscopy

Robust adaptive estimation of nonlinear system with time‐varying parameters

On‐line parameter estimation for a class of time‐varying continuous systems with bounded disturbances

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