On properties of optimal controls for an inverted spherical pendulum
Larisa Manita, Mariya Ronzhina
TL;DR
This paper investigates optimal control strategies for stabilizing an inverted spherical pendulum near its unstable equilibrium, revealing solutions with controls performing infinite rotations and achieving stabilization in finite time.
Contribution
It introduces a novel class of optimal controls involving infinite rotations for stabilization, expanding understanding of control behaviors near unstable equilibria.
Findings
Optimal controls perform infinite rotations along the circle.
Stabilization is achieved in finite time.
Solutions relate to the system's affine control structure.
Abstract
In this paper we study an optimal control problem that is affine in two-dimensional bounded control. The problem is related to the stabilization of an inverted spherical pendulum in the vicinity of the upper unstable equilibrium. We find solutions stabilizing the pendulum in a finite time, wherein the corresponding optimal controls perform an infinite number of rotations along the circle .
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Taxonomy
TopicsStability and Controllability of Differential Equations · Control and Stability of Dynamical Systems · Navier-Stokes equation solutions