A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm

Seeber, Richard; Horn, Martin; Fridman, Leonid

doi:10.1109/tac.2018.2812789

Cited by 74 publications

(49 citation statements)

References 15 publications

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“…Theorem 1: Consider system (2) with given positive parameters k 1 , k 2 and non-negative perturbation bounds K, L. Using the abbreviations A ∈ R 2×2 and e 1 , e 2 ∈ R 2 in (8), define the matrix M(P, Q, Θ 1 , Θ 2 ) as in (9) and the matrix…”

Section: Resultsmentioning

confidence: 99%

“…with the matrix M defined in (9), by applying the Schur complement. To furthermore eliminate the bilinearity κP, note that for any positive scalar λ one has…”

Section: A Optimization Problemmentioning

confidence: 99%

“…Obtaining upper bounds for it is important, especially when disturbances are present, because these may otherwise delay convergence in a prohibitive way. Such bounds have extensively been studied in literature, see, e.g., [6], [7], [8], [9]. In [9], these approaches are compared.…”

Section: Introductionmentioning

confidence: 99%

“…Such bounds have extensively been studied in literature, see, e.g., [6], [7], [8], [9]. In [9], these approaches are compared. Each imposes certain restrictions on the perturbations, and the bounds differ in conservativeness.…”

Section: Introductionmentioning

confidence: 99%

“…Each imposes certain restrictions on the perturbations, and the bounds differ in conservativeness. For small perturbations, the tightest bounds are obtained with the approach recently proposed in [9], which is based on a reaching time computation for the unperturbed case. Regarding perturbations, it is more restrictive than [7], however, which is based on a family of Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

Seeber

Horn

2019

IEEE Control Syst. Lett.

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The super-twisting algorithm is a second order sliding mode control law commonly used for robust control and observation. One of its key properties is the finite time it takes to reach the sliding surface. Using Lyapunov theory, upper bounds for this reaching time may be found. This contribution considers the problem of finding the best bound that may be obtained using a family of quadratic Lyapunov functions. An optimization problem for finding this bound is derived, whose solution may be obtained using semidefinite programming. It is shown that the restrictions imposed on the perturbations and the conservativeness of the obtained bound are significantly reduced compared to existing results from literature.

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Section: Resultsmentioning

confidence: 99%

“…with the matrix M defined in (9), by applying the Schur complement. To furthermore eliminate the bilinearity κP, note that for any positive scalar λ one has…”

Section: A Optimization Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

Seeber

Horn

2019

IEEE Control Syst. Lett.

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On phase deficit of the super‐twisting second‐order sliding mode control algorithm

Boiko

2020

Intl J Robust & Nonlinear

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The notion of phase deficit was introduced in [12], which allows one to determine if a nonlinear system can reveal finite-time or asymptotic convergence. Twisting and suboptimal second-order sliding mode control algorithms and a conventional relay feedback system were analyzed from the perspective of the phase deficit. However, phase deficit for the super-twisting algorithm was not determined at that time due to the complexity of the problem. Therefore, although it is known that the super-twisting algorithm reveals finite-time convergence (when no parasitic dynamics are present), it was not supported by the criterion based on the phase deficit. In the current article this problem has been solved through an open-loop interpretation of the phase deficit, which is proposed in the article. Another problem addressed in the article is the relationship between the frequency characteristics of the system and the type of convergence (finite-time or asymptotic). The mechanism of convergence is analyzed through considering time-varying frequency of self-excited oscillations and phase lag of the linear part of the system.

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Saturated exponential super‐twisting sliding mode control for bottom‐following of biomimetic underwater vehicles with unmeasured velocities

Gao,

Qin,

et al. 2023

Intl J Robust & Nonlinear

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This article addresses the bottom‐following problem for biomimetic underwater vehicles without translational velocity measurements in the presence of complex uncertainties and actuator saturation. A novel saturated exponential super‐twisting algorithm based integral terminal sliding mode control (SESTA‐ITSMC) scheme is created to ensure fast convergence and strong robustness as well as attenuate the chattering of actuators. Salient features are as follows. Instead of discontinuous term in the conventional super‐twisting algorithm, a novel SESTA is developed by incorporating a fractional power term, which ensures that the system achieves a faster transient response, effectively eliminating the chattering phenomenon. Then, to deal with the unknown states and further improve the anti‐interference ability of the system, the finite‐time dual estimator is devised to fast and precisely estimate the translational velocities and lumped uncertainties. Finally, a finite‐time anti‐windup auxiliary system is proposed to compensate for the saturation constraints on actuators in real time. Finite‐time convergence of estimation errors and bottom following errors is guaranteed by the Lyapunov stability theory. Comparative simulation results fully demonstrate the excellence of the proposed SESTA‐ITSMC scheme.

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A Novel Method to Estimate the Reaching Time of the Super-Twisting Algorithm

Cited by 74 publications

References 15 publications

Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

Optimal Lyapunov-Based Reaching Time Bounds for the Super-Twisting Algorithm

On phase deficit of the super‐twisting second‐order sliding mode control algorithm

Saturated exponential super‐twisting sliding mode control for bottom‐following of biomimetic underwater vehicles with unmeasured velocities

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