Nonlinear Hamiltonian Systems Under Sampling
Nonlinear Hamiltonian Systems Under Sampling
复制标题
采样下的非线性哈密顿系统
DOI：
10.1109/tac.2022.3164985
复制
发表时间：
2022
影响因子：
6.8
通讯作者：
Alessio Moreschini
中科院分区：
文献类型：
--
作者：
S. Monaco;D. Normand;M. Mattioni;Alessio Moreschini
本文研究了采样下哈密顿结构的变换。它示出了一个给定的端口哈密顿连续时间动态的精确采样等效模型表现出离散时间表示的离散梯度，具有相同的能量函数，但修改的阻尼和互连矩阵。通过构造，所提出的采样数据动态保证了在所有采样时刻的状态演化和能量平衡的精确匹配。将其推广到端口受控哈密顿动力学，得到了一个新的功率共轭输出，从而恢复了平均钝化的概念。在此基础上，提出能量管理控制策略。一个充满活力的解释的方法证实了其制定的狄拉克形式主义。通过两个典型算例验证了本文提出的采样数据建模方法的有效性。
This article investigates the transformation of Hamiltonian structures under sampling. It is shown that the exact sampled equivalent model associated to a given port-Hamiltonian continuous-time dynamics exhibits a discrete-time representation in terms of the discrete gradient, with the same energy function but modified damping and interconnection matrices. By construction, the proposed sampled-data dynamics guarantees exact matching of both the state evolutions and the energy-balance at all sampling instants. Its generalization to port-controlled Hamiltonian dynamics leads to characterize a new power conjugate output so recovering the concept of average passivation. On these bases, energy-management control strategies can be proposed. An energetic interpretation of the approach is confirmed by its formulation in the Dirac formalism. Two classical examples are worked out to validate the proposed sampled-data modeling in a comparative way with the literature.