On properties of optimal controls for an inverted spherical pendulum

2019/09/10 by Larisa Manita, Manita, Larisa, Mariya Igorevna Ronzhina +1
Engineering · Mathematics · #34H05 #34H15 #49N10 #49N90 #Control and Stability of Dynamical Systems #FOS: Mathematics #Navier-Stokes equation solutions #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1909.04708

openalex publication_date 2019/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S¹.

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