Generalised multivariable supertwisting algorithm

López‐Caamal, Fernando; Moreno, Jaime A.

doi:10.1002/rnc.4311

Cited by 25 publications

(41 citation statements)

References 35 publications

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“…Although note that these methods only ensure convergence to a boundary layer of the sliding manifold. Alternatively, the structure of (2) may also allow (depending on the disturbance) for the possibility of utilizing multivariable supertwisting algorithms 16,23 …”

Section: Invariant Subspace‐based Switching Function Design For Lti Systemsmentioning

confidence: 99%

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Robust orbital stabilization: A Floquet theory–based approach

Sætre¹,

Shiriaev

Freidovich

et al. 2021

Intl J Robust & Nonlinear

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The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance‐free system, a robustifying feedback extension is designed utilizing the sliding‐mode control (SMC) methodology. The main contribution of the article is to provide a constructive procedure for designing the time‐invariant switching function used in the SMC synthesis. More specifically, its zero‐level set (the sliding manifold) is designed using a real Floquet–Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a transverse linearization. This ensures asymptotic stability of the periodic orbit when the system is confined to the sliding manifold, despite any system uncertainties and external disturbances satisfying a matching condition. The challenging task of oscillation control of the underactuated cart–pendulum system subject to both matched‐ and unmatched disturbances/uncertainties demonstrates the efficacy of the proposed scheme.

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Section: Invariant Subspace‐based Switching Function Design For Lti Systemsmentioning

confidence: 99%

“…However, such an approximation can only ensure convergence to a boundary layer of the sliding manifold. Exploring alternative continuous sliding mode controllers, such as variants of the supertwisting algorithm, 16,23 is therefore of interest.…”

Section: Concluding Remarks and Future Directionsmentioning

confidence: 99%

Robust orbital stabilization: A Floquet theory–based approach

Sætre¹,

Shiriaev

Freidovich

et al. 2021

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Furthermore, under the assumptions made in [23] and [25], which represent the most general conditions presented on the literature, the only way to deal with the dry friction model is to assume that it has a bounded time derivative, i.e., that…”

Section: Motivation Examplementioning

confidence: 99%

“…Therefore, to design the controller gains, the bounds of the accelerations need to be known a priori. It is important to remark that the works presented in [21], [23]- [25] do not consider this algebraic loop.…”

Section: Motivation Examplementioning

confidence: 99%

“…However, the presence of an uncertain input matrix is not considered. Two kinds of MGSTAs were introduced in [22] and [23], including the one proposed by [21] that is termed unitary (or quasi-continuous), since the control terms are divided by the norm of the states. In [24] conditions on the (unitary) MGSTA gains are given to ensure the global finite-time convergence despite of an unknown but constant and symmetric input matrix and Lipschitz perturbations.…”

mentioning

confidence: 99%

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Multivariable Super-Twisting Algorithm for Systems with Uncertain Input Matrix and Perturbations

Moreno¹,

Luis²

2021

Preprint

Self Cite

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This paper proposes a Lyapunov approach to the design of a multivariable generalized Super-Twisting algorithm (MGSTA), which is able to control a system with perturbations and uncertain control matrix, both depending on time and the system states. The presented procedure shows that, under reasonable assumptions for the uncertainties, it is always possible to find a set of constant gains for the MGSTA in order to ensure global and robust finite-time stability of the system's outputs. Simulation results on an omnidirectional mobile robot illustrate the performance of the MGSTA.

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Multivariable variable‐gain super‐twisting control via output feedback for systems with arbitrary relative degrees

Rodrigues

Oliveira

2022

Adaptive Control & Signal

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An output-feedback super-twisting algorithm (STA) with variable gains is developed for multiple-input and multiple-output plants with arbitrary relative degrees. Global or semi-global finite-time exact tracking can be guaranteed for a class of uncertain systems with matched nonlinear time-varying disturbances, possibly dependent on the unmeasured states. This represents a significant generalization of recently introduced versions of the STAs to a multivariable setup with arbitrary relative degrees, output-feedback, and variable gains. The construction of such controller is based on a higher-order sliding-mode multivariable differentiator with dynamic gains. The gain adaptation for the controller and differentiator employs state-norm observers to overcome the lack of the full-state measurement. The stability properties of the proposed control system are demonstrated by means of input-to-state stability tools and a Lyapunov function-based analysis. The theoretical results are verified through numerical and academic examples.

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Generalised multivariable supertwisting algorithm

Cited by 25 publications

References 35 publications

Robust orbital stabilization: A Floquet theory–based approach

Robust orbital stabilization: A Floquet theory–based approach

Multivariable Super-Twisting Algorithm for Systems with Uncertain Input Matrix and Perturbations

Multivariable variable‐gain super‐twisting control via output feedback for systems with arbitrary relative degrees

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