论文标题
哈米尔顿港系统和单调性
Port-Hamiltonian systems and monotonicity
论文作者
论文摘要
探索了哈米尔顿港系统建模与单调性概念之间的关系。较早引入的增量港口 - 哈米尔顿系统的概念扩展到最大周期性单调关系以及它们的生成功能。这引起了新的渐进式 - 哈米尔顿港系统的新类别，其中源于物理系统建模以及凸优化的示例。对最大单调和最大循环单调关系的组成进行了深入的处理，在后一种情况下，所得的最大循环单调关系被证明是通过使用生成函数来计算的。此外，与被动性的增量版本讨论了连接，并显示了严格凸出的哈密顿量（最大）平衡独立的被动被动的渐进式 - 哈米尔顿港系统。最后，采用单调关系组成的结果用于凸优化方法，以计算相互联系的渐进式 - 港口港口系统的平衡。
The relationships between port-Hamiltonian systems modeling and the notion of monotonicity are explored. The earlier introduced notion of incrementally port-Hamiltonian systems is extended to maximal cyclically monotone relations, together with their generating functions. This gives rise to new classes of incrementally port-Hamiltonian systems, with examples stemming from physical systems modeling as well as from convex optimization. An in-depth treatment is given of the composition of maximal monotone and maximal cyclically monotone relations, where in the latter case the resulting maximal cyclically monotone relation is shown to be computable through the use of generating functions. Furthermore, connections are discussed with incremental versions of passivity, and it is shown how incrementally port-Hamiltonian systems with strictly convex Hamiltonians are (maximal) equilibrium independent passive. Finally, the results on compositionality of monotone relations are employed for a convex optimization approach to the computation of the equilibrium of interconnected incrementally port-Hamiltonian systems.
