Parameter identification in structured discrete-time uncertainties without persistency of excitation

Djaneye-Boundjou, Ouboti; Ordóñez, Raúl

doi:10.1109/ecc.2015.7331018

Cited by 7 publications

(6 citation statements)

References 7 publications

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“…This result completely coincides with the obtained results in [20] and even supports the continuoustime framework studies in [2,4,26]. Therefore, while applying the proposed FTCL, the data recording algorithm in [25] is used, where the appropriate data is selected to maximize λ min pSq λmaxpSq . Remark 2: In approximators with non-zero MFAE (εpkq ‰ 0), maximizing λ min pSq λmaxpSq , using the data recording algorithm in [25], helps to respectively enlarge and reduce the amplitudes of a and c that leads to narrow down the error bound in (36), whereas maximizing λ min pSq λmaxpSq matches with the concepts of concurrent learning in continuous-time [2,26].…”

Section: ) Adaptive Approximators With Non-zero Mfaes (εPkq ‰ 0)supporting

confidence: 87%

“…In all cases, the initial values and the controllers are all set to zero. A small exponential sum of sinusoidal input is injected to the system controller for ensuring the rank condition on the collected data and the data selection procedure in [25] is employed for both FTCL and concurrent learning methods. To fairly compare the speed and precision of the intended on-line learning methods for approximating f pxq and ĝpxq on the whole domain of x as time evolves, the following learning errors are computed on-line.…”

Section: Simulation Results and Discussionmentioning

confidence: 99%

“…The following theorem demonstrates the finite-time convergence properties of the proposed learning method. It should be noted that in the proposed FTCL method, the stored data in M and other stacks is selected based on data recording algorithm in [25] to maximize λ min pSq λmaxpSq where S " ř P h"1 dpτ h q dT pτ h q, and due to the satisfaction of M rank condition, S ą 0.…”

Section: Finite-time Convergent Analysis For the Proposed Ftclmentioning

confidence: 99%

“…Therefore, while applying the proposed FTCL, the data recording algorithm in [25] is used, where the appropriate data is selected to maximize λ min pSq λmaxpSq . Remark 2: In approximators with non-zero MFAE (εpkq ‰ 0), maximizing λ min pSq λmaxpSq , using the data recording algorithm in [25], helps to respectively enlarge and reduce the amplitudes of a and c that leads to narrow down the error bound in (36), whereas maximizing λ min pSq λmaxpSq matches with the concepts of concurrent learning in continuous-time [2,26]. Furthermore, choosing P " p `q (satisfying P ě pp `qq) not only helps to maximize λ min pSq λmaxpSq [25], but also, keeps c small.…”

Section: ) Adaptive Approximators With Non-zero Mfaes (εPkq ‰ 0)mentioning

confidence: 99%

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Nonlinear Discrete-time System Identification without Persistence of Excitation: Finite-time Concurrent Learning Methods

Tatari¹,

Panayiotou²,

Polycarpou³

2021

Preprint

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This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. A finitetime concurrent learning approach is presented to approximate the uncertainties of the discrete-time nonlinear systems in an on-line fashion by employing current data along with recorded experienced data satisfying an easy-to-check rank condition on the richness of the recorded data which is less restrictive in comparison with persistence of excitation condition. Rigorous proofs guarantee the finite-time convergence of the estimated parameters to their optimal values based on a discrete-time Lyapunov analysis. Compared with the existing work in the literature, simulation results illustrate that the proposed method can timely and precisely approximate the uncertainties.

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Section: ) Adaptive Approximators With Non-zero Mfaes (εPkq ‰ 0)supporting

confidence: 87%

Section: Simulation Results and Discussionmentioning

confidence: 99%

Section: Finite-time Convergent Analysis For the Proposed Ftclmentioning

confidence: 99%

Section: ) Adaptive Approximators With Non-zero Mfaes (εPkq ‰ 0)mentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Discrete-time System Identification without Persistence of Excitation: Finite-time Concurrent Learning Methods

Tatari¹,

Panayiotou²,

Polycarpou³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…which is a linear parametric model [27], [4] in the form of structured measurable uncertainty, and x, F ∈ R . The unknown parameter vector θ * ∈ R p will be estimated online, and its estimate is denoted θ(k) ∈ R p .…”

Section: A Stand-alone Parameter Estimationmentioning

confidence: 99%

A Discrete Fractional Order Adaptive Law for Parameter Estimation and Adaptive Control

Aburakhis

Ordóñez

Djaneye-Boundjou

2022

IEEE Open J. Control. Syst.

Self Cite

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In this article, a discrete fractional order adaptive law (DFOAL) is designed based on the Caputo fractional difference to perform parameter estimation of structured uncertainties. The paper provides a rigorous stability analysis of the DFOAL parameter estimation method. The DFOAL is then modified in order to improve parameter estimator performance to show that, under certain conditions, it provides asymptotic convergence to the true parameter values even when the regressor is not persistently exciting. A method to allow for practical implementation of the DFOAL and the modified DFOAL is developed. Finally, the modified DFOAL is used to identify the plant parameters in an indirect adaptive control law for a class of nonlinear discrete-time systems with structured uncertainty.

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Composite adaptation and learning for robot control: A survey

Guo

2023

Annual Reviews in Control

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Parameter identification in structured discrete-time uncertainties without persistency of excitation

Cited by 7 publications

References 7 publications

Nonlinear Discrete-time System Identification without Persistence of Excitation: Finite-time Concurrent Learning Methods

Nonlinear Discrete-time System Identification without Persistence of Excitation: Finite-time Concurrent Learning Methods

A Discrete Fractional Order Adaptive Law for Parameter Estimation and Adaptive Control

Composite adaptation and learning for robot control: A survey

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