The equivalence of controlled Lagrangian and controlled Hamiltonian systems

被引:110
作者
Chang, DE [1 ]
Bloch, AM
Leonard, NE
Marsden, JE
Woolsey, CA
机构
[1] CALTECH, Pasadena, CA 91125 USA
[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
[3] Princeton Univ, Princeton, NJ 08544 USA
[4] Virginia Tech, Blacksburg, VA 24061 USA
关键词
controlled Lagrangian; controlled Hamiltonian; energy shaping; Lyapunov stability; passivity; equivalence;
D O I
10.1051/cocv:2002045
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity) on the Hamiltonian side, which is the Hamiltonian counterpart of a class of gyroscopic forces on the Lagrangian side.
引用
收藏
页码:393 / 422
页数:30
相关论文
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