Robust Disturbance Rejection by the Attractive Ellipsoid Method – Part II: Discrete-time Systems

García, Pablo Ruipérez; Ampountolas, Konstantinos

doi:10.1016/j.ifacol.2018.11.360

Cited by 9 publications

(6 citation statements)

References 8 publications

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“…Proof 1. In the first part of the proof, we shall follow a procedure similar to the one in [32]. Consider a Lyapunov function…”

Section: Resultsmentioning

confidence: 99%

Robust disturbance rejection for discrete-time systems having Magnitude and rate bounded inputs

Küçükdemiral

2020

Journal of the Franklin Institute

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The design of a robust controller for uncertain discrete-time systems subject to bounded disturbances and having magnitude and rate bounded actuators is considered. To tackle the problem, the proposed method utilises nested ellipsoids and employs an incremental (velocity) form of the state-space model of the system. By using modified full block S-procedure, the proposed robust control design approach is applicable to any uncertain system with rational parameter dependence which cannot be managed by the existing approaches without introducing some extra conservatism. Finally, an algorithm that allows the method to be used as a gain-scheduling controller is also noted in the study.

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“…Proof 1. In the first part of the proof, we shall follow a procedure similar to the one in [32]. Consider a Lyapunov function…”

Section: Resultsmentioning

confidence: 99%

Robust disturbance rejection for discrete-time systems having Magnitude and rate bounded inputs

Küçükdemiral

2020

Journal of the Franklin Institute

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“…By the S-procedure, if (15) holds with P ≻ 0 and τ1 , τ2 , and τ3 nonnegative, then σ (1) 0 (𝜉(k)) ≥ 0 whenever σ1 (𝜉(k)) ≥ 0, σ2 (𝜉(k)) ≥ 0, and σ3 (𝜉(k)) ≥ 0. Similarly, if (16) holds with P ≻ 0, Q ≻ 0, and τ4 , τ5 , and τ6 nonnegative, then σ (2) 0 (𝜉(k)) ≥ 0 whenever σ1 (𝜉(k)) ≥ 0, σ2 (𝜉(k)) ≥ 0, and σ3 (𝜉(k)) ≥ 0. To conclude, σ2 (𝜉(k)) ≥ 0 since 𝚫 ∈ pwIQC(Ψ, S), σ3 (𝜉(k)) ≥ 0 since d(k) ∈  Λ , and σ1 (𝜉(k)) ≥ 0 by assumption.…”

Section: And Y T (K) Qy(k) ≤ 1 If and Only If σ(1)mentioning

confidence: 99%

Computation of invariant sets for discrete‐time uncertain systems

Khalife

Jaoude

Farhood

et al. 2023

Intl J Robust & Nonlinear

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This article proposes novel methods for the computation of state and output bounding sets for discrete‐time uncertain systems. The systems under consideration are formed from the interconnection of a nominal linear time‐invariant system and an uncertainty operator that is known to lie within a prespecified set. The set of allowable uncertainties is described by a pointwise integral quadratic constraint (IQC), that is, a quadratic constraint that holds for all time‐steps. Examples of pointwise IQCs characterizing common uncertainty sets are provided. The exogenous input to the system is assumed to lie in a given polytope or ellipsoid for all time‐steps. The proposed methods are illustrated via an example.

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“…At present, active fault diagnosis research for closed-loop system mainly designs an optimal auxiliary signal and a control law according to some indexes and specific methods to guarantee incipient faults detection and isolation. 33,34 In order to guarantee incipient fault diagnosis, we need to design an auxiliary signal to separate the zonotopes in healthy and faulty cases. The auxiliary signal has an influence on system performance that causes a larger tracking error of the healthy system output to the reference input.…”

Section: Introductionmentioning

confidence: 99%

“…In order to meet the actual industrial needs and solve actual production safety problems, active fault diagnosis methods for the closed‐loop system need to be deeply investigated. At present, active fault diagnosis research for closed‐loop system mainly designs an optimal auxiliary signal and a control law according to some indexes and specific methods to guarantee incipient faults detection and isolation 33,34 . In order to guarantee incipient fault diagnosis, we need to design an auxiliary signal to separate the zonotopes in healthy and faulty cases.…”

Section: Introductionmentioning

confidence: 99%

An integrated design method for active fault diagnosis and control

Jing

Zhou

et al. 2023

Intl J Robust & Nonlinear

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The injection of an auxiliary input signal for active fault diagnosis may cause the change of system control performance in closed-loop operation. This paper presents a novel integrated design method for active fault diagnosis and tracking control in order to facilitate the detection of incipient faults, meanwhile ensuring the normal operation of the closed-loop system. First, a zonotopic filter is generated based on P radius minimization method to estimate the uncertain bound set of systems states. Then, an auxiliary input signal is designed to separate the reachable sets of the system in healthy and faulty operation situations.Generally, the auxiliary input signal is required to be designed minimizing the system closed-loop performance degradation. In this paper, a tracking controller is designed altogether with the auxiliary input signal to make the system output track a given reference. An optimal index is proposed to minimize simultaneously the energy of the auxiliary input signal and the output tracking error. Next, a fault detection logic is provided based on checking whether the closed-loop system state belongs to healthy zonotope. Finally, the feasibility and advantages of this work are verified by means of a numerical example.

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Robust Disturbance Rejection by the Attractive Ellipsoid Method – Part II: Discrete-time Systems

Cited by 9 publications

References 8 publications

Robust disturbance rejection for discrete-time systems having Magnitude and rate bounded inputs

Robust disturbance rejection for discrete-time systems having Magnitude and rate bounded inputs

Computation of invariant sets for discrete‐time uncertain systems

An integrated design method for active fault diagnosis and control

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