Robust exact differentiators with predefined convergence time

Seeber, Richard; Haimovich, Hernan; Horn, Martin; Battista, Hernán De

doi:10.1016/j.automatica.2021.109858

Cited by 49 publications

(48 citation statements)

References 25 publications

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“…This procedure generalizes to an arbitrary order and arbitrary degrees that proposed in [20] for the first order differentiator with d 0 = −1. Note that this scaling, using two parameters, is novel also for the homogeneous case.…”

Section: Convergence Acceleration and Scaling The Lipschitz Constant ∆mentioning

confidence: 80%

“…In [13] also a switching strategy between homogeneous differentiators with restricted degrees is presented. This work can be seen as an extension to an arbitrary order of the smooth strategy of combining two homogeneous differentiators proposed in [14], [15], [16], and in the recent work [20]. Our construction extends to the discontinuous case the recursive observer design developed for continuous homogeneous observers in [23], [24] and highly improved in [12], [25] for continuous bl-homogeneous observers.…”

mentioning

confidence: 93%

“…n = 2) this property has been obtained in [14], [15], [16], [17], using quadratic-like Lyapunov functions [18], [19]. This approach for the discontinuous firstorder differentiator has been extended and refined in [20], where a detailed gain scaling has been developed and a tight convergence time estimation has been obtained, using the results of [21]. For differentiators of arbitrary order this can be achieved by using a switching strategy between two homogeneous differentiators of positive and negative degrees, as it is proposed in [22].…”

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confidence: 99%

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Arbitrary Order Fixed-Time Differentiators

Moreno¹

2020

Preprint

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Differentiation is an important task in control, observation and fault detection. Levant's differentiator is unique, since it is able to estimate exactly and robustly the derivatives of a signal with a bounded high-order derivative. However, the convergence time, although finite, grows unboundedly with the norm of the initial differentiation error, making it uncertain when the estimated derivative is exact. In this paper we propose an extension of Levant's differentiator so that the worst case convergence time can be arbitrarily assigned independently of the initial condition, i.e. the estimation converges in Fixed-Time. We propose also a family of continuous differentiators and provide a unified Lyapunov framework for analysis and design. I. INTRODUCTIONGiven a (Lebesgue-measurable) signal f (t) defined on [0, ∞) the objective of a differentiator is to estimate as close as possible some of its time derivatives. Usually, signal f (t) is composed of the base signal f 0 (t), which we want to differentiate and is assumed to be n-times differentiable, and a noise signal ν(t), that we will assume to be uniformly bounded, i.e. f (t) = f 0 (t) + ν(t).

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Section: Convergence Acceleration and Scaling The Lipschitz Constant ∆mentioning

confidence: 80%

mentioning

confidence: 93%

mentioning

confidence: 99%

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Arbitrary Order Fixed-Time Differentiators

Moreno¹

2020

Preprint

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“…Remark 4 (Conservatism of the prescribed UBST) The estimated UBST of the finite-time or fixed-time ESOs [38][39][40][41] is conservative. By contrast, the newly proposed prescribed-time differentiators [42,43] realized significantly reduced slack between the actual settling time and the estimated UBST. The proposed PTESO (5) further reduces the conservatism compared to the differentiators [42,43].…”

Section: Prescribed-time Stability Analysismentioning

confidence: 93%

“…At present, few attempted to develop a prescribed-time extended state observer (PTESO). Rodrigo Aldana-Lopez et al [42] and Seeber et al [43] realized the prescribed-time stability (PTS) of robust exact differentiators, which are used to observe the first-order derivative of time-varying signals but cannot be treated as an ESO. Two prescribed-time state observers were proposed in [44,45] for unperturbed systems.…”

Section: Introductionmentioning

confidence: 99%

Continuous Prescribed-Time Sliding Mode Control with A Prescribed-Time ESO for Second-Order Nonlinear Systems with Mismatched Disturbance

Wang

Guan

et al. 2021

Preprint

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This paper aims to settle the continuous prescribed-time stabilization problem of second-order nonlinear systems with mismatched disturbances. A continuous prescribed-time sliding mode control (CPTSMC) method with a prescribed-time extended state observer (PTESO) is proposed. The PTESO can precisely estimate the unknown states and disturbances, with its upper bound for the settling time (UBST) prescribed by only one parameter more tightly than existing finite-time or fixed-time ESOs. Furthermore, as a common concern for ESOs, the peaking value problem is well addressed. Then, a novel prescribed-time convergent form with little conservatism and simple tuning procedures is designed, and the internal mechanism in acquiring higher transient performance is explicitly researched. By using the estimated states and disturbances, the CPTSMC makes system states converge in a chattering-alleviated manner following the novel prescribed-time form. In addition to proving that the UBST of the whole system is tightly prescribed by only one design parameter, we show the continuity of the CPTSMC and the boundedness of all system signals, which are vital for practical applications. Ultimately, numerical simulations on the second-order system and a DC motor servo verify the efficiency of the proposed control system.

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Predefined‐time tracking control for high‐order nonlinear systems with control saturation

Gong

Guo

et al. 2022

Intl J Robust & Nonlinear

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In this paper, an innovative predefined‐time tracking control algorithm is proposed for high‐order nonlinear systems with control saturation and disturbance, which can directly calculate the upper bound of settling‐time by user‐defined parameters. First, a predefined‐time observer based on tracking differentiator is applied to handle the disturbance. Next, a new predefined‐time tracking control algorithm is designed using the backstepping method, and a novel auxiliary dynamic system is designed to deal with the control saturation. The stability of the closed‐loop system is analyzed applying Lyapunov function‐like method. The derivative of the virtual controller is obtained by the first‐order filter to reduce the computation burden. It is worth mentioning that, different from the exiting results, all parameters related to settling‐time in each virtual controller can be selected differently, and it can improve the flexibility of the controller design. Finally, the robustness and effectiveness of the investigated algorithm have been demonstrated by two typical numerical simulations.

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Robust exact differentiators with predefined convergence time

Cited by 49 publications

References 25 publications

Arbitrary Order Fixed-Time Differentiators

Arbitrary Order Fixed-Time Differentiators

Continuous Prescribed-Time Sliding Mode Control with A Prescribed-Time ESO for Second-Order Nonlinear Systems with Mismatched Disturbance

Predefined‐time tracking control for high‐order nonlinear systems with control saturation

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