Finite-time stabilisation of simple mechanical systems using continuous feedback

Sanyal, Amit K.; Bohn, Jan

doi:10.1080/00207179.2014.974675

Cited by 50 publications

(30 citation statements)

References 8 publications

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“…Equations (20) and (21) κ . It can be proven by analysis similar to Steps 1) and 2) that the reduced system obtained from (20) and (21) is uniformly bounded according to Assumption 2.1. Lemma 2.1 can then be used to confirm uniform local finite-time stability of the equilibria in 1 E .…”

Section: Gftac With Full-state Measurementsmentioning

confidence: 99%

“…Finite-time stable systems usually demonstrate fast convergence rates and significant disturbance rejection properties [11][12][13][14]. Given these properties, finite-time attitude regulators were constructed in [15] via a fractional-power feedback domination approach, in [16] by the terminal sliding mode (TSM) method, in [17,18] by homogeneous theory, and in [19] by a TSM-like method proposed in [20] for simple mechanical systems. None of these control laws, however, ensures global stability.…”

Section: Introductionmentioning

confidence: 99%

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Global finite-time attitude tracking via quaternion feedback

Gui

Vukovich

2016

Systems & Control Letters

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This paper addresses the attitude tracking of a rigid body using a quaternion description. Global finite-time attitude controllers are designed with three types of measurements, namely, full states, attitude plus constant-biased angular velocity, and attitude only. In all three scenarios hybrid control techniques are utilized to overcome the well-known topological constraint on the attitude manifold, while coupled nonsmooth feedback inputs are designed via homogeneous theory to achieve finitetime stability. Specially, a finite-time bias observer is derived in the second scenario and a quaternion filter is constructed to provide damping in the absence of velocity feedback. The proposed methods ensure bounded control torques a priori and, in particular, include several existing attitude controllers as special cases.

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Section: Gftac With Full-state Measurementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global finite-time attitude tracking via quaternion feedback

Gui

Vukovich

2016

Systems & Control Letters

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“…The approach in is extended and applied to the dynamics of a rigid body rotating under the action of a control torque and an unknown external moment. This extension, in going from a mechanical system represented by generalized coordinates in

{double-struckR}^{n}

to attitude dynamics on the configuration space SO(3), is non‐trivial, because SO(3) is non‐contractible unlike

{double-struckR}^{n}

.…”

Section: Almost Global Finite‐time Stabilization Of Rigid Body Attitumentioning

confidence: 99%

“…Note that the signum function is not needed in the definition of the control torque, unlike the schemes in , for example, because the powers of only positive‐definite quantities occur in the control law, the Lyapunov function, and its time derivative along the feedback system. This is a practically useful property that follows from the framework given in for continuous finite‐time stabilization of mechanical systems with multiple degrees of freedom. The following result gives an equivalent asymptotically stable feedback stabilization scheme that is obtained from the finite‐time stabilization scheme of Theorem in the limiting case of p = 1.Proposition Let

α = \frac{1}{p}

and consider the control law when evaluated in the limit that α = 1.…”

Section: Finite‐time Attitude Stabilizationmentioning

confidence: 99%

“…This makes continuous finite‐time stabilizing control schemes appealing for applications requiring guaranteed convergence and robustness properties while being implementable with actuators that can only provide continuous control inputs . While the work in dealt with continuous finite‐time control schemes and the work in dealt with double integrator dynamics, a constructive way to obtain continuous finite‐time stabilizing control for mechanical systems with multiple degrees of freedom appeared recently in . Extending the framework in , a finite‐time stabilization scheme is formulated here for attitude stabilization on the tangent bundle of SO(3), using the Hölder continuous Morse–Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

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Almost global finite-time stabilization of rigid body attitude dynamics using rotation matrices

Bohn

Sanyal

2015

Int. J. Robust. Nonlinear Control

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Summary This work considers continuous finite‐time stabilization of rigid body attitude dynamics using a coordinate‐free representation of attitude on the Lie group of rigid body rotations in three dimensions, SO(3). Using a Hölder continuous Morse–Lyapunov function, a finite‐time feedback stabilization scheme for rigid body attitude motion to a desired attitude with continuous state feedback is obtained. Attitude feedback control with finite‐time convergence has been considered in the past using the unit quaternion representation. However, it is known that the unit quaternion representation of attitude is ambiguous, with two antipodal unit quaternions representing a single rigid body attitude. Continuous feedback control using unit quaternions may therefore lead to the unstable unwinding phenomenon if this ambiguity is not resolved in the control design, and this has adverse effects on actuators, settling time, and control effort expended. The feedback control law designed here leads to almost global finite‐time stabilization of the attitude motion of a rigid body with Hölder continuous feedback to the desired attitude. As a result, this control scheme avoids chattering in the presence of measurement noise, does not excite unmodeled high‐frequency structural dynamics, and can be implemented with actuators that can only provide continuous control inputs. Numerical simulation results for a spacecraft in low Earth orbit, obtained using a Lie group variational integrator, confirm the theoretically obtained stability and robustness properties of this attitude feedback stabilization scheme. Copyright © 2015 John Wiley & Sons, Ltd.

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A robustness study of a finite‐time/exponential tracking continuous control scheme for constrained‐input mechanical systems: Analysis and experiments

Zamora-Gómez

Zavala‐Río

Vázquez‐Ramírez

et al. 2020

Intl J Robust & Nonlinear

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The closed-loop analysis of a recently proposed continuous scheme for the finite-time or exponential tracking control of constrained-input mechanical systems is reformulated under the consideration of an input-matching bounded perturbation term. This is motivated by the poor number of works devoted to support the so-cited argument claiming that continuous finite-time controllers are more robust than asymptotical (infinite-time) ones under uncertainties and the limitations of their results. We achieve to analytically prove that, for a perturbation term with sufficiently small bound, the considered tracking continuous control scheme leads the closed-loop error variable trajectories to get into an origin-centered ball whose radius becomes smaller in the finite-time convergence case, entailing smaller posttransient variations than in the exponential case. Moreover, this is shown to be achieved for any initial condition, avoiding to restrain any of the parameters involved in the control design, and under the suitable consideration of the nonautonomous nature of the closed loop. The study is further corroborated through experimental tests on a multi-degree-of-freedom robotic manipulator, which do not only confirm the analytical result but also explore the scope or limitations of its conclusions under adverse perturbation conditions. K E Y W O R D Sconstrained inputs, input-matching perturbation, mechanical systems, robustness, tracking continuous control, uniform finite-time stability INTRODUCTIONControl synthesis aiming at the accomplishment of a regulation or trajectory tracking goal in finite time through continuous feedback has been the subject of intensive research in the last years. Numerous works with such a design objective formulation have been motivated arguing benefits of the finite-time algorithms over the asymptotic (infinite-time) ones, such as faster convergence and improved robustness under uncertainties. [1][2][3][4] However, this has not yet been exhaustively explored or brought to the fore through formal analysis or implementation tests. The only analysis treating one of those aspects, that the authors are aware of, was developed by Bhat and Bernstein, 5 who studied the robustness issue. More Int J Robust Nonlinear Control. 2020;30:3923-3944. wileyonlinelibrary.com/journal/rnc

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Finite-time stabilisation of simple mechanical systems using continuous feedback

Cited by 50 publications

References 8 publications

Global finite-time attitude tracking via quaternion feedback

Global finite-time attitude tracking via quaternion feedback

Almost global finite-time stabilization of rigid body attitude dynamics using rotation matrices

A robustness study of a finite‐time/exponential tracking continuous control scheme for constrained‐input mechanical systems: Analysis and experiments

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