Finite-Time Stabilization via Sliding Mode Control

Song, Jun; Niu, Yugang; Zou, Yuanyuan

doi:10.1109/tac.2016.2578300

Cited by 230 publications

(103 citation statements)

References 15 publications

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“…. Therefore, | x(t) | decreases and reaches the value | x(t) |= for a time T 1 ≤ 1 2 (p−1) p−1 , which corresponds to the first term in (4). Note that this term expression is independent of an unknown initial condition x 0 .…”

Section: Discussionmentioning

confidence: 94%

“…Step A ends with | x(T 1 ) |= > 0. If | x 0 |≤ , Step A is not executed; therefore, the term 1 2 (p−1) p−1 would be absent in (4). B.…”

Section: Discussionmentioning

confidence: 99%

“…∕(1 − Mh( 1 )∕ 1 )m, which, after dividing both parts of the fraction by M, corresponds to the former terms in (4). The optimal value of is determined [26] minimizing the first two terms in (4) with respect to .…”

Section: Discussionmentioning

confidence: 99%

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Continuous Fixed‐Time Convergent Super‐Twisting Algorithm in Case of Unknown State and Disturbance Initial Conditions

Rodriguez‐Ramirez

Garza-Alonso

2018

Asian Journal of Control

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This paper presents a fixed-time convergent super-twisting-like algorithm designed to provide a direct extension, without any additional terms, of the conventional super-twisting control system, whose state initial condition is unknown and the disturbance initial condition is bounded by a known constant or even completely unknown. The fixed-time convergent super-twisting-like algorithm is first designed for a scalar system and then generalized to a multivariable one. An upper estimate of its convergence (settling) time is calculated in each case. Several examples are provided to illustrate the obtained theoretical results.

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Section: Discussionmentioning

confidence: 94%

“…Step A ends with | x(T 1 ) |= > 0. If | x 0 |≤ , Step A is not executed; therefore, the term 1 2 (p−1) p−1 would be absent in (4). B.…”

Section: Discussionmentioning

confidence: 99%

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Continuous Fixed‐Time Convergent Super‐Twisting Algorithm in Case of Unknown State and Disturbance Initial Conditions

Rodriguez‐Ramirez

Garza-Alonso

2018

Asian Journal of Control

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“…Sliding mode control (SMC) is particularly well suited for situations where unknown non‐linearities affect the system, as in the case of USMs. In recent years, numerous results have been reported on the SMC for various complex dynamical systems (see, e.g., ). For underwater vehicles, in general, some important contributions are given in .…”

Section: Introductionmentioning

confidence: 99%

Trajectory Tracking for Underwater Swimming Manipulators using a Super Twisting Algorithm

Borlaug

Gravdahl

Sverdrup-Thygeson

et al. 2018

Asian Journal of Control

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The underwater swimming manipulator (USM) is a snake-like, multi-articulated, underwater robot that is equipped with thrusters. One of the main purposes of the USM is to act like an underwater floating base manipulator. As such, it is essential to achieve good station-keeping and trajectory tracking performance for the USM by using the thrusters and by using the joints to attain the desired position and orientation of the head and tail of the USM. In this 'paper, we propose a sliding mode control (SMC) law, specifically the super-twisting algorithm with adaptive gains, for the trajectory tracking of the USM's centre of mass. A higher-order sliding mode observer is proposed for state estimation. Furthermore, we show the ultimate boundedness of the tracking errors. We demonstrate the applicability of the proposed control law and show that it leads to better performance than a linear PD-controller.

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“…For instance, in the work of Li and Cao, the finite‐time stochastically stability problem was investigated for Markovian jump memristive neural networks. In the work of Song et al, the sliding‐mode control design problem based on FTB had been studied for nonlinear systems. Zhao et al had proposed finite‐time H ∞ control for a class of Markovian jump delayed systems.…”

Section: Introductionmentioning

confidence: 99%

Reliable finite‐time H_∞ control for singular Markovian jump system with actuator saturation via sliding‐mode approach

Liu

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper explores the finite‐time H∞ control problem for singular stochastic systems with actuator saturation and time‐varying state delay through the sliding‐mode approach. Time delay is a kind of positive differentiable bounded delay. A novel suitable switching function and a suitable sliding‐mode control law are given to guarantee that the closed‐loop actuator saturating system is singular stochastic H∞ finite‐time boundedness on the specified sliding surface. Sensor failures are taken into consideration for the error system, and sufficient criteria are provided to ensure the error system is singular stochastic finite‐time boundedness. The gain matrices of sliding‐mode controller and state observer are obtained by solving the corresponding linear matrix inequalities. Finally, simulation examples are given to illustrate the proposed method.

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Finite-Time Stabilization via Sliding Mode Control

Cited by 230 publications

References 15 publications

Continuous Fixed‐Time Convergent Super‐Twisting Algorithm in Case of Unknown State and Disturbance Initial Conditions

Continuous Fixed‐Time Convergent Super‐Twisting Algorithm in Case of Unknown State and Disturbance Initial Conditions

Trajectory Tracking for Underwater Swimming Manipulators using a Super Twisting Algorithm

Reliable finite‐time H_∞ control for singular Markovian jump system with actuator saturation via sliding‐mode approach

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Finite-Time Stabilization via Sliding Mode Control

Cited by 230 publications

References 15 publications

Continuous Fixed‐Time Convergent Super‐Twisting Algorithm in Case of Unknown State and Disturbance Initial Conditions

Continuous Fixed‐Time Convergent Super‐Twisting Algorithm in Case of Unknown State and Disturbance Initial Conditions

Trajectory Tracking for Underwater Swimming Manipulators using a Super Twisting Algorithm

Reliable finite‐time H∞ control for singular Markovian jump system with actuator saturation via sliding‐mode approach

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Reliable finite‐time H_∞ control for singular Markovian jump system with actuator saturation via sliding‐mode approach