Integral Sliding Mode Convex Optimization in Uncertain Lagrangian Systems Driven by PMDC Motors: Averaged Subgradient Approach

Poznyak, Alexander S.; Nazin, Alexander; Alazki, Hussain

doi:10.1109/tac.2020.3032088

Cited by 15 publications

(15 citation statements)

References 15 publications

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“…The finite time convergence to a neighborhood of the equilibrium point is proven. In [6] an algorithm is developed which is based on the convex optimization concept applied to a dynamic plant modeled using the Lagrangian ap-proach, given by a differential standard equation of the second ordinary order and with unknown right-hand side, but with accessible states, as well as their speeds. Article [7] developed a finite-time optimal formation tracking for planar vehicles technique with holonomics dynamics, using Pontryagin's maximum principle on a Lie group.…”

Section: Brief Surveymentioning

confidence: 99%

ASG version of integral sliding mode robust controller for AV nonholonomic 2D models avoiding obstacles

2022

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Section: Brief Surveymentioning

confidence: 99%

ASG version of integral sliding mode robust controller for AV nonholonomic 2D models avoiding obstacles

2022

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“…Recent investigations have considered designing SM controller using the average sub gradient method to get the minimization of functional depending on the tracking error for Lagrangian systems without exact model. 16 On-line optimization of a non-strictly convex functional can be made using the sub-gradient approach, 17 which yields proposing a broader class of extreme seeking control design using the SM control approach. The implementation of average sub-gradient control simplifies the controller structure, but requires the precise calculus of the uncertain sections associated with the studied Lagrangian dynamics.…”

Section: Brief Surveymentioning

confidence: 99%

“…The practical implementation of the suggested ISMC requires the application of modifications for the controller, including variants of the ideas proposed in studies. 29–31 In particular, the study introduced in Blidberg 4 served to develop a well-defined practical variant for the ISMC, but simplifying the fractional derivative implementation.…”

Section: Control Formulationmentioning

confidence: 99%

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Output feedback averaged sub-gradient integral sliding mode control to regulate the tridimensional autonomous motion of autonomous submersible vehicles

Hernández-Sánchez

Poznyak

Andrianova

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part I:

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This study presents the development of an output feedback control for regulating the movement of an autonomous submersible vehicles in the tridimensional space. The controller formulation applies the Averaged Sub-Gradient Integral Sliding Mode which is fed with the estimation of the translational velocity states by a distributed super-twisting algorithm. The structure of the autonomous submersible vehicles dynamics permits the implementation of the ASG algorithm using the estimates of translation velocity. The proposed scheme solves a non-linear extremum seeking problem that aims to minimize a non-strictly convex function that depends on the tracking error defined by the difference of some suitable reference trajectories and the coordinates of the submarine center of mass. The desired reference trajectories were designed to force the autonomous submersible vehicles three-dimensional motion to a continuous circuit in an oscillating shape over the horizontal plane combined with a submersion on the z-axis. The comparison between the proposed controller, the ASG with complete knowledge of the states and the state feedback controller is presented. This comparison confirms the output feedback ASG controller forced the autonomous submersible vehicles to the desired trajectory with a notable difference in the magnitude of the control given the estimation of the states. These outcomes justify the potential contributions of the suggested ASG integrated with the super-twisting algorithm to obtain the local minimization of the evaluated functional depending on the tracking error. The results justify the potential contributions of the suggested ASG with the super-twisting algorithm to regulate the position of the autonomous submersible vehicles to the desired trajectory.

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“…10 This technique uses an optimization strategy, which is based on technical stability fundamentals. Recent studies have proposed the application of the averaged sub-gradient (ASG) methodology to obtain the closed-loop optimization of Lagrangian systems with uncertain mathematical models (including external perturbations and uncertain modeling) such as the study proposed in Poznyak et al 11 The inclusion of sub-gradient technique allows to include non-strict convex functional to be optimized. This condition simplifies the controller design, but requires the accurate estimation of the uncertain component of the analyzed Lagrangian dynamics.…”

Section: Introductionmentioning

confidence: 99%

Robust dynamic backstepping averaged sub-gradient integral sliding mode control for navigation of mobile robots

Sanchez

Poznyak

Andrianova

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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The main goal of the current investigation is to present an output feedback robust control that regulates the motion of mobile robotic autonomous devices based on the application of the dual averaged sub-gradient descendant method. Sub-gradient realization aims to solve the design of a proposed extremum seeking control to stabilize the trajectory tracking error between the three-dimensional position of mobile robotic autonomous devices and some attainable reference trajectories in the same spatial domain. The controller belongs to a class of sliding mode controller with variable gain based on a sliding surface depending on the tracking error and its time derivative. This derivative is estimated with the application of a distributed time-dependent super-twisting robust differentiator. The proposed mobile robotic autonomous device dynamics considers the dynamics of actuators (direct current motors) which drives the mobilization of mobile robotic autonomous devices. The dynamic nature of the mobile robotic autonomous devices regulated by motor actuators induces a backstepping-like controller design based on a two-stage sequential application of the sub-gradient strategy, one for the mobile robotic autonomous devices and the second for the motor dynamics. The mixed strategy appears as a novel formulation to solve the path track for reference trajectories of mobile robotic systems. The proposed control considers the optimization of the tracking error dependent functional without the full knowledge of the mobile robotic autonomous device dynamics. With the aim of proving the effectiveness of the suggested design, two numerical examples are developed. In these examples, the tracking performance, minimization of the proposed functional as well as control evolution are evaluated. The controlled tracking outcomes of the proposed integral sliding mode control are contrasted with the outcomes produced by a set of proportional–derivative and selected sliding mode (first-order type) controllers. The suggested controller shows a superior tracking of the reference trajectory than the other two comparative controllers, using quality measures such as least mean square error and its integral.

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Integral Sliding Mode Convex Optimization in Uncertain Lagrangian Systems Driven by PMDC Motors: Averaged Subgradient Approach

Cited by 15 publications

References 15 publications

ASG version of integral sliding mode robust controller for AV nonholonomic 2D models avoiding obstacles

ASG version of integral sliding mode robust controller for AV nonholonomic 2D models avoiding obstacles

Output feedback averaged sub-gradient integral sliding mode control to regulate the tridimensional autonomous motion of autonomous submersible vehicles

Robust dynamic backstepping averaged sub-gradient integral sliding mode control for navigation of mobile robots

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