Analysis and Loop-Shaping of Holomorphic Dynamical PDE Systems*

机译：储物动力学PDE系统的分析和环形成形*

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Holomorphic Dynamical systems is a class of infinite dimensional systems with a infinite number of zeros and no poles. Systems in this class are always BIBO stable with an exact finite settling time for the step response, because they are in feedforward mode, without any inherent feedback physical mechanism. In this paper a precise definition of Holomorphic Dynamical systems is given along with a stability result. Time solutions are also discussed and its control is addressed. This kind of systems are often present in PDE modelling of mass and energy transport phenomena for industrial plant units. Examples and one control application are presented, illustrating the approach described.

机译：全象动态系统是一类无限尺寸系统，具有无限数量的零，没有杆。本类中的系统始终是BiBo稳定，具有精确的有限度稳定时间，用于阶跃响应，因为它们处于前馈模式，而没有任何固有的反馈物理机制。在本文中，给出了稳定性的稳定性动力系统的精确定义。还讨论了时间解决方案，并解决了其控制。这种系统通常存在于工业设备单元的质量和能量传输现象的PDE建模中。提出了示例和一个控制应用，示出了描述的方法。

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《Mediterranean Conference on Control and Automation》|2021年|621-626|共6页
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J.M. Igreja; J.M. Lemos;
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Computational modeling; Optimal control; Predictive models; Stability analysis; Frequency response; Industrial plants; Dynamical systems;

机译：计算建模;最优控制;预测模型;稳定性分析;频率响应;工厂;动态系统;

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1. The Briot-Bouquet systems and the center families for holomorphic dynamical systems [J] . Rong F. Advances in Mathematics . 2013,第1期

机译：Briot-Bouquet系统和全纯动力系统的中心族
2. Asymptotic analysis for a class of infinite systems of first-order PDE: Nonlinear parabolic PDE in the singular limit [J] . Ishii H., Shimano K. Communications in Partial Differential Equations . 2003,第1a2期

机译：一阶PDE无限系统的渐近分析：奇异极限的非线性抛物线PDE
3. Quasiconformal homeomorphisms and dynamics III. The Teichmuller space of a holomorphic dynamical system [J] . McMullen CT., Sullivan DP. Advances in Mathematics . 1998,第2期

机译：准同形同胚与动力学III。全纯动力系统的Teichmuller空间
4. Discrete Holomorphic Local Dynamical Systems [C] . Marco Abate C.I.M.E. Summer School . 2010

机译：离散的全象局部动态系统
5. Sparse Collocation Methods for Solving High Dimension PDES in Estimation and Control of Dynamical Systems. [D] . Mercurio, Michael. 2017

机译：动态系统估计和控制中解决高维PDES的稀疏配置方法。
6. The auxiliary region method: a hybrid method for coupling PDE- and Brownian-based dynamics for reaction–diffusion systems [O] . Cameron A. Smith, Christian A. Yates 2018

机译：辅助区域法：一种用于反应扩散系统的基于PDE和布朗氏动力学耦合的混合方法
7. INDICES AND RESIDUES OF HOLOMORPHIC VECTOR FIELDS ON SINGULAR VARIETIES(Topology of Holomorphic Dynamical Systems and Related Topics) [O] . SUWA TATSUO 1996

机译：奇异矢量场的奇异向量场的指标和残差（全纯动力系统拓扑及相关主题）
8. Topological Invariants of Dynamical Systems and Spaces of Holomorphic Maps. Part211 1 [R] . Gromov, M. 1999

机译：动力系统的拓扑不变量和全纯映射的空间。 part211 1

Analysis and Loop-Shaping of Holomorphic Dynamical PDE Systems*

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