Minimal Differential Difference Realizations of Delay Differential, Differential Difference, and Neutral Delay Systems
Minimal Differential Difference Realizations of Delay Differential, Differential Difference, and Neutral Delay Systems
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DOI：
10.1109/lcsys.2020.3038758
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发表时间：
2021-10
影响因子：
3
通讯作者：
M. Peet
中科院分区：
文献类型：
--
作者：
M. Peet
时延微分方程 (DDE) 通常用于表示对大型网络的控制。然而，延迟的存在使得此类网络的分析和控制问题变得具有挑战性。最近，微分差分方程（DDF）被提出作为一种建模框架，它使我们能够更有效地表示网络或大规模延迟系统中延迟通道的低维性质。然而不幸的是，从 DDE 到 DDF 的标准转换公式并没有考虑到这种低维结构 - 因此大型延迟网络或系统的任何有效的 DDF 表示都必须手工制作。在这封信中，我们提出了一种用于构建 DDE 和 DDF 系统的 DDF 实现的算法，其中延迟通道的维度已被最小化。此外，我们提供了这些算法的便捷 PIETOOLS 实现，并表明该算法显着降低了几个说明性示例（包括中性延迟系统（NDS））的模型复杂性。
Delay-Differential Equations (DDEs) are often used to represent control of and over large networks. However, the presence of delay makes the problems of analysis and control of such networks challenging. Recently, Differential Difference Equations (DDFs) have been proposed as a modelling framework which allows us to more efficiently represent the low-dimensional nature of delayed channels in a network or large-scale delayed system. Unfortunately, however, the standard conversion formulae from DDE to DDF do not account for this low-dimensional structure - hence any efficient DDF representation of a large delayed network or system must be hand-crafted. In this letter, we propose an algorithm for constructing DDF realizations of both DDE and DDF systems wherein the dimension of the delayed channels has been minimized. Furthermore, we provide a convenient PIETOOLS implementation of these algorithms and show that the algorithm significantly reduces the complexity of the model for several illustrative examples, including Neutral Delay Systems (NDSs).