Stabilizability of Controlled Lagrangian Systems of Two Degrees of Freedom and One Degree of Under-Actuation by the Energy-Shaping Method
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Abstract
We provide some criteria for stabilizability by the energy-shaping method for the class of all controlled Lagrangian systems of two degrees of freedom and one degree of under-actuation: a necessary and sufficient condition for Lyapunov stabilizability, two sufficient conditions for asymptotic stabilizability, and a necessary and sufficient condition for exponential stabilizability. As a corollary, we show that some of the asymptotically stabilizing controllers that were designed in old literatures with the energy-shaping method are actually exponentially stabilizing controllers. Examples of such systems are the inverted pendulum on a cart, the Furuta pendulum, the ball and beam system, and the Pendubot.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
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| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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