Passivity, port-hamiltonian formulation and solution estimates for a coupled magneto-quasistatic system

IF 1.3 4区 数学 Q1 MATHEMATICS
Timo Reis, T. Stykel
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引用次数: 1

Abstract

We study a~quasilinear coupled magneto-quasistatic model from a~systems theoretic perspective.} First, by taking the injected voltages as input and the associated currents as output, we prove that the magneto-quasistatic system is passive. Moreover, by defining suitable Dirac and resistive structures, we show that it admits a~representation as a~port-Hamiltonian system. Thereafter, we consider dependence on initial and input data. We show that the current and the magnetic vector potential can be estimated by means of the initial magnetic vector potential and the voltage. We also analyse the free dynamics of the system and study the asymptotic behavior of the solutions for $t\to\infty$.
耦合磁-准静态系统的无源性、端口-哈密顿公式和解估计
从系统理论的角度研究了准线性耦合磁-准静态模型。首先,我们以注入电压为输入,以相关电流为输出,证明了磁准静态系统是无源的。此外,通过定义合适的狄拉克结构和电阻结构,我们证明了它可以表示为一个波特-哈密顿系统。然后,我们考虑对初始数据和输入数据的依赖性。我们证明了电流和磁矢势可以通过初始磁矢势和电压来估计。我们还分析了系统的自由动力学,并研究了$t\to\infty$解的渐近行为。
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来源期刊
Evolution Equations and Control Theory
Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.10
自引率
6.70%
发文量
5
期刊介绍: EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology
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