Time optimal swing-up of the planar pendulum

Paolo Mason; Mireille Broucke; Benedetto Piccoli

doi:10.1109/TAC.2008.929391

Time optimal swing-up of the planar pendulum

Paolo Mason, Mireille Broucke, Benedetto Piccoli

Research output: Contribution to journal › Article › peer-review

46 Scopus citations

Abstract

This paper presents qualitative results on the global structure of the time optimal trajectories of the planar pendulum on a cart. This mechanical system is a benchmark to test nonlinear control methods and various papers addressed the problem of computing time optimal open-loop controls. Relying on the theory of optimal synthesis, we provide a discontinuous feedback giving optimal solutions for any initial data. The approach is that of geometric control theory.

Original language	English (US)
Pages (from-to)	1876-1886
Number of pages	11
Journal	IEEE Transactions on Automatic Control
Volume	53
Issue number	8
DOIs	https://doi.org/10.1109/TAC.2008.929391
State	Published - 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Keywords

Inverted pendulum
Stabilization
Time optimal control

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10.1109/TAC.2008.929391

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title = "Time optimal swing-up of the planar pendulum",

abstract = "This paper presents qualitative results on the global structure of the time optimal trajectories of the planar pendulum on a cart. This mechanical system is a benchmark to test nonlinear control methods and various papers addressed the problem of computing time optimal open-loop controls. Relying on the theory of optimal synthesis, we provide a discontinuous feedback giving optimal solutions for any initial data. The approach is that of geometric control theory.",

keywords = "Inverted pendulum, Stabilization, Time optimal control",

author = "Paolo Mason and Mireille Broucke and Benedetto Piccoli",

note = "Funding Information: Manuscript received April 20, 2007; revised December 1, 2007. Current version published September 24, 2008. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC), SISSA, Trieste, and IECN/INRIA, Nancy. Recommended by Associate Editor D. Dochain.",

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AU - Broucke, Mireille

AU - Piccoli, Benedetto

N1 - Funding Information: Manuscript received April 20, 2007; revised December 1, 2007. Current version published September 24, 2008. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC), SISSA, Trieste, and IECN/INRIA, Nancy. Recommended by Associate Editor D. Dochain.

PY - 2008

Y1 - 2008

N2 - This paper presents qualitative results on the global structure of the time optimal trajectories of the planar pendulum on a cart. This mechanical system is a benchmark to test nonlinear control methods and various papers addressed the problem of computing time optimal open-loop controls. Relying on the theory of optimal synthesis, we provide a discontinuous feedback giving optimal solutions for any initial data. The approach is that of geometric control theory.

AB - This paper presents qualitative results on the global structure of the time optimal trajectories of the planar pendulum on a cart. This mechanical system is a benchmark to test nonlinear control methods and various papers addressed the problem of computing time optimal open-loop controls. Relying on the theory of optimal synthesis, we provide a discontinuous feedback giving optimal solutions for any initial data. The approach is that of geometric control theory.

KW - Inverted pendulum

KW - Stabilization

KW - Time optimal control

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ER -

Time optimal swing-up of the planar pendulum

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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