Symplectic feedback using Hamiltonian Lie algebra and its applications to an inverted pendulum

被引：0

作者：

Espiro J.L. ^{[1
]}

Poblete C.M. ^{[2
]}

机构：

[1] Departamento de Ciencias Fisicas, Facultad de Ingenieria, Ciencias y Administracion, Universidad de La Frontera, Temuco, Avenida Francisco Salazar 01145

[2] Departamento de Ingenieria Electrica, Facultad de Ingenieria, Ciencias y Administracion, Universidad de La Frontera, Temuco, Avenida Francisco Salazar 01145

来源：

Journal of Control Theory and Applications | 2013年 / 11卷 / 02期

关键词：

Geometric control; Hamiltonian systems; Lie algebra; Nonlinear dynamical systems; Symplectic structures;

D O I：

10.1007/s11768-013-1073-7

中图分类号：

学科分类号：

摘要：

From the symplectic representation of an autonomous nonlinear dynamical system with holonomic constraints, i. e., those that can be represented through a symplectic form derived from a Hamiltonian, we present a new proof on the realization of the symplectic feedback action, which has several theoretical advantages in demonstrating the uniqueness and existence of this type of solution. Also, we propose a technique based on the interpretation, construction and characterization of the pull-back differential on the symplectic manifold as a member of a one-parameter Lie group. This allows one to synthesize the control law that governs a certain system to achieve a desired behavior; and the method developed from this is applied to a classical system such as the inverted pendulum. © 2013 South China University of Technology, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.

引用

页码：275 / 281

页数：6

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