Optimal Synthesis in the Control Problem of an n-Link Inverted Pendulum with a Moving Base

Manita, Larisa; Ronzhina, Mariya

doi:10.1007/s10958-017-3222-x

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…Chattering singularities may occur in the problem of swinging up the pendulum by energy controls [5]. It was shown that there are optimal chattering controls in the problem for an n-link inverted pendulum on a movable base (cart), in which the control is a bounded scalar force applied to the base [32]. Namely, for the linearized model it was proved that in a small neighborhood of the origin, the optimal solutions are as follows: in finite time the nonsingular trajectories with an infinite number of switchings of the control attain the singular second-order surface, and then the trajectory with singular control remains on the singular surface, asymptotically approaching the origin with increasing time.…”

Section: 3mentioning

confidence: 99%

Optimal spiral-like solutions near a singular extremal in a two-input control problem

Manita¹,

Ronzhina²

2021

DCDS-B

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<p style='text-indent:20px;'>We study an optimal control problem affine in two-dimensional bounded control, in which there is a singular point of the second order. In the neighborhood of the singular point we find optimal spiral-like solutions that attain the singular point in finite time, wherein the corresponding optimal controls perform an infinite number of rotations along the circle <inline-formula><tex-math id="M1">\begin{document}$ S^{1} $\end{document}</tex-math></inline-formula>. The problem is related to the control of an inverted spherical pendulum in the neighborhood of the upper unstable equilibrium.</p>

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Section: 3mentioning

confidence: 99%

Optimal spiral-like solutions near a singular extremal in a two-input control problem

Manita¹,

Ronzhina²

2021

DCDS-B

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“…However, it was proved that it is possible to turn this position into a stable one, for example, if the suspension point of a planar pendulum performs vertical oscillations [5,6] or moves along a horizontal line (e.g. [7][8][9]). It turns out that motions of a spherical inverted pendulum can also be stabilized by choosing an appropriate external control, e.g.…”

Section: Introductionmentioning

confidence: 99%