Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The 3-D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom; it is acted on by gravity and it is fully actuated by control forces. In , almost global stabilization of the inverted equilibrium manifold was studied using a smooth globally defined feedback. Here,  study the problem of almost global stabilization of the inverted equilibrium manifold using non-smooth feedback of angular velocity and a reduced attitude vector of the 3-D pendulum. The importance of the non-smooth feedback is that the almost global domain of attraction is a geometrically simple set that excludes the hanging attitude manifold. Unlike the closed-loop for a 3-D pendulum with a smooth controller, the closed-loop designed in this paper does not exhibit a performance constraint. These new results are based on Lyapunov analysis of the non-smooth closed-loop 3-D pendulum.
['Nalin Chaturvedi', 'N. Harris McClamroch']
I am writing a research paper on a idea Asymptotic Stabilization of the Inverted Equilibrium Manifold of the 3-D Pendulum Using Non-Smooth Feedback
[{"from": "human", "value": "I am writing a research paper on a idea Asymptotic Stabilization of the Inverted Equilibrium Manifold of the 3-D Pendulum Using Non-Smooth Feedback"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The 3-D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom; it is acted on by gravity and it is fully actuated by control forces. In , almost global stabilization of the inverted equilibrium manifold was studied using a smooth globally defined feedback. Here,  study the problem of almost global stabilization of the inverted equilibrium manifold using non-smooth feedback of angular velocity and a reduced attitude vector of the 3-D pendulum. The importance of the non-smooth feedback is that the almost global domain of attraction is a geometrically simple set that excludes the hanging attitude manifold. Unlike the closed-loop for a 3-D pendulum with a smooth controller, the closed-loop designed in this paper does not exhibit a performance constraint. These new results are based on Lyapunov analysis of the non-smooth closed-loop 3-D pendulum."}]