Gradient-Based Discrete-Time Concurrent Learning for Standalone Function Approximation

Djaneye-Boundjou, Ouboti; Ordóñez, Raúl

doi:10.1109/tac.2019.2920087

Cited by 20 publications

(11 citation statements)

References 21 publications

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“…Maximizing λ min pSq λmaxpSq (maximizing λ min pSq and minimizing λmaxpSq) also leads to enlarging aγ which causes faster settling-time in (66). 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 .…”

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

confidence: 87%

“…Theorem 1: Consider the approximator for nonlinear system (1) given by ( 14), whose parameters are adjusted according to the update law of (20) with the regressor given by (11). Let Assumptions 1-2 hold, once the rank condition on M and…”

Section: Finite-time Convergent Analysis For the Proposed Ftclmentioning

confidence: 99%

“…are met, then 1) for adaptive approximators with zero MFAE, i.e., εpkq " 0, the proposed parameter update law (20) guarantees that Θpkq converges to zero within finite time steps; 2) for adaptive approximators with non-zero MFAE, i.e., εpkq ‰ 0, (}εpkq} ď bε), the proposed parameter update law (20) guarantees that Θpkq is ultimately bounded, Θpkq ď b Θ, in finite time steps, with the ultimate bound…”

Section: Finite-time Convergent Analysis For the Proposed Ftclmentioning

confidence: 99%

“…Hence, it is of great practical importance to investigate finite-time learning of discrete-time systems. There are only a few results discussing the identification of discrete-time systems including [19,20]. The work of [19], studied the discrete-time systems uncertainty identification in finite-time, where the proposed method required the on-line invertibility check of a regressor matrix and its inverse computation, along with interval excitation of the regressor.…”

Section: Introductionmentioning

confidence: 99%

“…The work of [19], studied the discrete-time systems uncertainty identification in finite-time, where the proposed method required the on-line invertibility check of a regressor matrix and its inverse computation, along with interval excitation of the regressor. In [20], a concurrent learning-based method for discrete-time function approximation is presented that relaxed the PE condition and guaranteed the asymptotic convergence and boundedness of the parameters estimation errors, respectively, for function approximators with zero and non-zero residual approximation errors in case of optimal parameters.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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: Finite-time Convergent Analysis For the Proposed Ftclmentioning

confidence: 99%

Section: Finite-time Convergent Analysis For the Proposed Ftclmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 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

Data‐driven optimal fault‐tolerant‐control and detection for a class of unknown nonlinear discrete‐time systems

Treesatayapun

2021

Optim Control Appl Methods

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The design of optimal fault-tolerant control with actuator and sensor faults is investigated. The system dynamics and faults are considered as a class of unknown nonlinear discrete-time systems when the data-driven equivalent model is formulated by a multi-input fuzzy rule emulated network (MiFREN).The multi-gradient learning law is developed with the proposed fault-detection algorithm to enchant the performance of MiFREN. By employing only pieces of information from the equivalent model, the proposed controller is designed and the closed-loop performance is analyzed through the rigorous theorem. Simulation systems and comparison results are provided to validate the performance of the proposed scheme.

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Adaptive anti‐disturbance sampling control of autonomous surface vehicles based on discrete‐time concurrent learning extended state observers

Cui

et al. 2023

Intl J Robust & Nonlinear

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Summary This paper investigates the surge speed tracking control of an autonomous surface vehicle (ASV) subject to fully unknown internal dynamic, external disturbance, and unknown control input gain. An adaptive anti‐disturbance sampling control method is proposed for an ASV without using any model parameters. Specifically, by utilizing real‐time and historical data, discrete‐time reduced‐order and full‐order concurrent learning extended state observers (CLESOs) are designed to estimate the unknown ASV model parameters and ensure estimation convergence without requiring persistent excitation. Then, a surge speed tracking control law is designed based on the discrete‐time full‐order CLESO. Through Lyapunov stability analysis, the closed‐loop system is proven to be stable, and the estimation and tracking errors are bounded. Simulation and hardware‐in‐loop experimental results validate the effectiveness of the proposed discrete‐time CLESOs for the surge speed tracking of an ASV with fully unknown dynamic model.

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Gradient-Based Discrete-Time Concurrent Learning for Standalone Function Approximation

Cited by 20 publications

References 21 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

Data‐driven optimal fault‐tolerant‐control and detection for a class of unknown nonlinear discrete‐time systems

Adaptive anti‐disturbance sampling control of autonomous surface vehicles based on discrete‐time concurrent learning extended state observers

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