A continuation theorem on periodic solutions of regular nonlinear systems and its application to the exact tracking problem for the inverted spherical pendulum
type: Item
instance of: scholarly article
title: A continuation theorem on periodic solutions of regular nonlinear systems and its application to the exact tracking problem for the inverted spherical pendulum
zbMATH Open document ID: 1216.34031
author: Luca Consolini
author: Mario Tosques
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-11-05T00:00:00Z
review text: The authors present a continuation method to obtain a family of \(T\)-periodic solutions \(\{x_s(\cdot)\}_{0\leq s < \delta}\) associated to a family of \(T\)-periodic systems \[ \dot{x}_s(t) = F(t,s,x_s(t))\quad \forall s \in [0,\delta), \] such that \[ x_0(\cdot) = \tilde{x}(\cdot), \] where \(\tilde{x}\) is an assigned \(T\)-periodic solution. The authors apply these conditions to the exact tracking problem for the inverted spherical pendulum. They consider the following problem: given an arbitrary \(T\)-periodic curve \(\gamma\in C^3({\mathbb R}, {\mathbb R}^3)\), find a control force \(f\in C({\mathbb R}, {\mathbb R}^3)\), such that, if \(x(0) = \gamma(0)\), then \(x(t) = \gamma(t)\) \(\forall t \geq 0\).
reviewed by: Jinzhi Lei
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5810935
zbMATH Keywords: continuation methods
zbMATH Keywords: periodic solutions
zbMATH Keywords: inverted spherical pendulum
MaRDI profile type: Publication
full work available at URL: j.na.2010.08.002
OpenAlex ID: W2019367008
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DOI: 10.1016/J.NA.2010.08.002
description: scientific article; zbMATH DE number 5810935