Generation of New Exciting Regressors for Consistent Online Estimation of Unknown Constant Parameters

Bobtsov, Alexey A.; Astolfi, Alessandro

doi:10.1109/tac.2022.3159568

Cited by 20 publications

(14 citation statements)

References 16 publications

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“…with tuning gains α > 0, f 0 > 0, β ≥ 0, M ≥ 1 f0 and γ > 0, and we used the definitions (6). Then, for all f 0 > 0, η 0 ∈ R q and θ 0 ∈ R q , we have that (7) holds with all signals bounded.…”

Section: Linearly Parameterized Regression Equationsmentioning

confidence: 99%

A New Least Squares Parameter Estimator for Nonlinear Regression Equations with Relaxed Excitation Conditions and Forgetting Factor

Romero¹,

Aranovskiy²

2022

Preprint

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In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it incorporates a forgetting factor allowing it to preserve alertness to time-varying parameters; (iii) thanks to the addition of a mixing step it relies on a set of scalar regression equations ensuring a superior transient performance; (iv) it is applicable to nonlinearly parameterized regressions verifying a monotonicity condition and to a class of systems with switched time-varying parameters; (v) it is shown that it is bounded-input-bounded-state stable with respect to additive disturbances; (vi) continuous and discrete-time versions of the estimator are given. The superior performance of the proposed estimator is illustrated with a series of examples reported in the literature.

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Section: Linearly Parameterized Regression Equationsmentioning

confidence: 99%

A New Least Squares Parameter Estimator for Nonlinear Regression Equations with Relaxed Excitation Conditions and Forgetting Factor

Romero¹,

Aranovskiy²

2022

Preprint

Self Cite

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“…To reveal the dynamics properties of the closed-loop system ( 23), (28), consider the function V(x e , y e , θ e , z 1 , z 2 ) = 1 2 (x 2 e + y 2 e + θ 2 e + z 2 1 + z 2 2 ), whose time-derivative along the extended system (23), (32) is given as…”

Section: Iandi Adaptive Tracking Control Of a Nonholonomic Mobile Robotmentioning

confidence: 99%

Adaptive control of a class of time-varying nonlinear systems via immersion and invariance

Liang

Liu

et al. 2022

Science Progress

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This paper addresses the adaptive control of a class of time-varying nonlinear systems. Under the framework of Immersion and Invariance (I&I) adaptive control, a set of sufficient conditions is obtained to stabilize the concerned time-varying nonlinear systems. It is shown that the presented controller can also be utilized to complete tracking control for a class of nonholonomic constraint systems if the desired trajectories satisfy certain conditions. The effectiveness of the new adaptive controller is demonstrated by some numerical simulations on a nonholonomic mobile robot.

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“…[7][8][9][10][11][12][13][14] Also, recently the energy pumping-and-damping injection principle 32 has been successfully applied to generate the PE regressor from the IE one. 18,19 In contrast to the above-considered adaptive laws that 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 References 20-23, 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.…”

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 time-invariant parameters. Their applicability to estimate the piecewise constant (PC) parameters is usually tested via numerical experiments only and, with a number of exceptions like References 13, 14, and 20, does not have a sufficiently rigorous analytical proof.…”

Section: Introductionmentioning

confidence: 99%

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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Generation of New Exciting Regressors for Consistent Online Estimation of Unknown Constant Parameters

Cited by 20 publications

References 16 publications

A New Least Squares Parameter Estimator for Nonlinear Regression Equations with Relaxed Excitation Conditions and Forgetting Factor

A New Least Squares Parameter Estimator for Nonlinear Regression Equations with Relaxed Excitation Conditions and Forgetting Factor

Adaptive control of a class of time-varying nonlinear systems via immersion and invariance

Unknown piecewise constant parameters identification with exponential rate of convergence

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