端口哈密顿系统的互联不具动力学性
Interconnection of port-Hamiltonian systems is not dynamical
AI总结：
本文研究端口哈密顿系统的互联问题，发现其互联不具动力学性，仅在常狄拉克结构或端口哈密顿ODE系统等常见情形下行为等价，对非常狄拉克结构给出了充分条件。
AI中文摘要：
端口哈密顿系统的互联通常被理解为保结构的，这源于几何事实：底层狄拉克结构的复合仍为狄拉克结构。逐点来看这无疑成立，但比较动力学系统时，通常会比较其轨迹，而轨迹需满足某些正则性假设。本文证明，经典解和弱解在互联端口哈密顿系统的解与实现该互联的动力学系统之间，未必存在一一对应关系。在研究最多的常狄拉克结构或端口哈密顿常微分方程系统情形下，二者行为等价；针对非常狄拉克结构，本文给出了一个充分条件。
英文摘要：
The interconnection of port-Hamiltonian systems is usually understood as structure-preserving due to the geometric fact that the composition of the underlying Dirac structures produces again a Dirac structure. Pointwise, this is doubtless true, but when comparing dynamical systems, their trajectories are usually compared, and trajectories usually obey some regularity assumptions. It is shown that both classical and weak solutions do not necessarily exhibit a one-to-one correspondence between solutions of the interconnected port-Hamiltonian system, and the dynamical system realising the interconnection. In the mostly studied cases of constant Dirac structures or port-Hamiltonian ODE systems, both systems are behaviourally equivalent; for non-constant Dirac structures, a sufficient condition is given.
