Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection
Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection
复制标题
无限维系统的哈密顿港公式 II。
DOI：
10.1109/cdc.2004.1429325
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
C. Melchiorri
中科院分区：
文献类型：
--
作者：
A. Macchelli;A. Schaft;C. Melchiorri
本文给出了关于端口哈密顿形式分布参数系统边界控制的一些新结果。通过推广有限维Dirac结构的概念，将经典的动力系统的有限维端口哈密顿公式推广到分布参数和多变量的情形，以处理无穷维幂变量空间。因此，似乎很自然，也有限维端口哈密顿系统开发的有限维控制方法可以扩展，以科普无限维系统。本文将互联控制和能量成形方法应用于分布参数系统的有限维控制器镇定问题。关键是将Casimir函数的定义推广到混合情形，即当动力系统是由无穷维和有限维部分的功率守恒互连所产生时。给出了一维热传导方程稳定化的一个简单应用。
In this paper, some new results concerning the boundary control of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system has been generalized to the distributed parameter and multivariable case by extending the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables. Consequently, it seems natural that also finite dimensional control methodologies developed for finite dimensional port Hamiltonian systems can be extended in order to cope with infinite dimensional systems. In this paper, the control by interconnection and energy shaping methodology is applied to the stabilization problem of a distributed parameter system by means of a finite dimensional controller. The key point is the generalization of the definition of Casimir function to the hybrid case, i.e. when the dynamical system to be considered results from the power conserving interconnection of an infinite and a finite dimensional part. A simple application concerning the stabilization of the one-dimensional heat equation is presented.