Predefined-time parameter estimation via modified dynamic Regressor extension and mixing

Wu, Zhonghua; Ma, Miao; Xu, Xiaozhuo; Liu, Bojun; Yu, Ziquan

doi:10.1016/j.jfranklin.2021.06.028

Cited by 9 publications

(11 citation statements)

References 49 publications

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“…A potential drawback of this algorithm is that it critically relies on the inclusion of a dynamic extension that mimicks the dynamics of the PEE, which may adversely affect the robustness of the estimator, [42,Remark 7] and [41]. A similar difficulty is present in the algorithm recently proposed in [56].…”

Section: Introductionmentioning

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: Introductionmentioning

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

View full text Add to dashboard Cite

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“…• ensure exponential convergence of the parameter error to zero under weak regressor excitation requirements 1,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] ;…”

Section: Introductionunclassified

“…In contrast to the above-considered adaptive laws, which require the data stack processing, this approach does not use offline operations, but, like the schemes [7][8][9][10][11][12][13][14] , has strong inertial properties. In [20][21][22][23] adaptive laws are proposed, which, unlike the previously considered ones, provide finite time identification of the RE unknown parameters if IE or FE condition is met. A more detailed review of some modern methods to relax the PE condition is given in 1 .…”

Section: Introductionmentioning

confidence: 99%

“…However, the laws [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] have been developed only to solve the identification problems of the RE time-invariant parameters. Their applicability to estimate the piecewise constant parameters is usually tested in numerical experiments only and, with a number of exceptions like 13,14,20 , does not have a sufficiently rigorous analytical proof.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the method in 42 ensures the piecewise constant unknown parameters tracking, which is its main advantage over other procedures to relax the PE requirement [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] . However, over time, the number of models used in 42 can increase indefinitely, and the necessity to adjust simultaneously all parameters of all models, as well as store, monitor and process a high number of data stacks, requires high computational power of the hardware in use.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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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

Predefined-time parameter estimation via modified dynamic Regressor extension and mixing

Cited by 9 publications

References 49 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

Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence

Unknown piecewise constant parameters identification with exponential rate of convergence

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