THE INVERSE PROBLEM OF THE CALCULUS OF VARIATIONS AND THE STABILIZATION OF CONTROLLED LAGRANGIAN SYSTEMS

被引：3

作者：

Farre Puiggali, M. ^{[1
]}

Mestdag, T. ^{[2
,3
]}

机构：

[1] UCM, UC3M, UAM, CSIC,Inst Ciencias Matemat, C Nicolas Cabrera 13-15, Madrid 28049, Spain

[2] Univ Antwerp, Dept Math & Comp Sci, Middelheimlaan 1, B-2020 Antwerp, Belgium

[3] Univ Ghent, Dept Math, Krijgslaan 281, B-9000 Ghent, Belgium

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2016年 / 54卷 / 06期

关键词：

controlled Lagrangians; inverse problem; stability; Lyapunov function; GENERALIZED HELMHOLTZ CONDITIONS;

D O I：

10.1137/16M1060091

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We apply methods of the so-called "inverse problem of the calculus of variations" to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the inverted pendulum on a cart and the inertia wheel pendulum. By making use of a condition that follows from Douglas' classification, we derive feedback controls for which the control system is variational. We then use the energy of a suitable controlled Lagrangian to provide a stability criterion for the equilibrium.

引用

页码：3297 / 3318

页数：22

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