Adaptive estimation for uncertain nonlinear systems with measurement noise: A sliding‐mode observer approach

Franco, Roberto; Ríos, Héctor; Efimov, Denis; Perruquetti, Wilfrid

doi:10.1002/rnc.5220

Cited by 18 publications

(29 citation statements)

References 29 publications

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“…Remark 1. Opposite to [19] and [20], the adaptive observer in (7) strikes systems with relative degree larger than one. For instance, mechanical systems, where the relative degree of the output (position), with respect to the external disturbance w(t) (in acceleration), is equal to two.…”

Section: Hosm Adaptive Observermentioning

confidence: 99%

“…Let us consider the Lyapunov function given in ( 9) that satisfies the inequalities (10) and (11). Following the procedure given in [20], the time derivative of V θ along the trajectories of the error dynamics (8), with α = 0, satisfies…”

Section: A the Nonlinear Parameter Identification Algorithmmentioning

confidence: 99%

“…given in (18), with c such that Vη < 0 in the sublevel set L c ; and then, from the sublevel set L c , the values for τ i can be computed as τ i = max Lc |η i |, for all i = 1, n. 4) Verify the small-gain condition (20). Note that the values for min and max depend on the excitation given by the term G(t, y, u) in (7a), which depends on the input u.…”

Section: ) Define the Setmentioning

confidence: 99%

“…Thus, it is possible to modify both min and max by means of the input. Note also that κ 1 , κ 2 and ψ can be adjusted to manipulate the left-hand side of (20).…”

Section: ) Define the Setmentioning

confidence: 99%

“…The proposed algorithm is included in the structure of a sliding-mode state observer, providing an ultimate bound for the full estimation error and attenuating the effects of the external disturbances concluding finite-time convergence of the identification error and exponential convergence of the estimation error. In [20], an adaptive observer based on [19] is developed, this observer increases the class of systems ensuring finite-time convergence of the parameter identification error and exponential convergence to a neighborhood of the state estimation error.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A High-Order Sliding-Mode Adaptive Observer for Uncertain Nonlinear Systems

Ríos¹,

Franco²,

Loza³

et al. 2023

IEEE Trans. Automat. Contr.

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A high-order sliding-mode adaptive observer is proposed to solve the problem of adaptive estimation, i.e., the simultaneous estimation of the state and parameters, for a class of uncertain nonlinear systems in the presence of external disturbances, that does not need to satisfy a relative degree condition equal to one. This approach is based on a highorder sliding-mode observer and a nonlinear parameter identification algorithm. The practical, global and uniform asymptotic stability of the adaptive estimation error, despite the external disturbances, is guaranteed through the small-gain theorem. The convergence proofs are developed based on Lyapunov and inputto-state stability theories. Some simulation results illustrate the performance of the proposed high-order sliding-mode adaptive observer.

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Section: Hosm Adaptive Observermentioning

confidence: 99%

Section: A the Nonlinear Parameter Identification Algorithmmentioning

confidence: 99%

Section: ) Define the Setmentioning

confidence: 99%

“…Thus, it is possible to modify both min and max by means of the input. Note also that κ 1 , κ 2 and ψ can be adjusted to manipulate the left-hand side of (20).…”

Section: ) Define the Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A High-Order Sliding-Mode Adaptive Observer for Uncertain Nonlinear Systems

Ríos¹,

Franco²,

Loza³

et al. 2023

IEEE Trans. Automat. Contr.

Self Cite

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Design of a joint adaptive observer for a class of affine nonlinear sampled‐output system with unknown states and parameters

Zhuang

Wang

Ali

et al. 2021

Adaptive Control & Signal

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Summary In this article, a joint adaptive observer design method is proposed for a class of affine nonlinear systems subject to sampled output data measurements. The considered class of system contains nonlinear terms which depend on unknown parameters. The considered unknown parameters enter the system in both the output and the system states equations which render the design of the sampled data observer for the affine nonlinear system more difficult to conceive. To solve this problem, and based on a new method of decoupling parameter estimation and state observation, a new online output sampling joint adaptive observer is proposed in this article, which can simultaneously guarantees the exponential convergence of the estimation of unknown state and parameter. The structure of the proposed observer has been extended to the case of sampled and delayed data measurements. To illustrate the performance of the proposed observer, a comparison is made with another observer with an output predictor on a satellite navigation system. And the observer proposed in this article is applied to the model‐free control of ultra‐local models.

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Parameter identification and state estimation for a diabetic glucose‐insulin model via an adaptive observer

Franco

Ríos

Loza

et al. 2022

Intl J Robust & Nonlinear

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In this article, an adaptive observer is designed for patients with Type 1 Diabetes Mellitus. The adaptive observer, synthesized using the so-called Bergman's Minimal Model, simultaneously estimates the states and the parameter corresponding to the insulin-independent glucose disappearance rate. The adaptive observer deals with parameter uncertainties, whereas the food intake is regarded as an external disturbance. The adaptive observer relies on intravenous glucose measurements. The state estimation error converges to a neighborhood of the origin despite the effects of the external disturbances and uncertainties, while the parameter estimation error converges in a fixed time to a neighborhood of the origin. The adaptive observer synthesis is given by a constructive method based on linear matrix inequalities. Simulation results show the feasibility of the proposed scheme. Moreover, the approach is validated in UVA/Padova metabolic simulator for ten in silico adult patients.

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Adaptive estimation for uncertain nonlinear systems with measurement noise: A sliding‐mode observer approach

Cited by 18 publications

References 29 publications

A High-Order Sliding-Mode Adaptive Observer for Uncertain Nonlinear Systems

A High-Order Sliding-Mode Adaptive Observer for Uncertain Nonlinear Systems

Design of a joint adaptive observer for a class of affine nonlinear sampled‐output system with unknown states and parameters

Parameter identification and state estimation for a diabetic glucose‐insulin model via an adaptive observer

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