SGER: AN INNOVATIVE FRAMEWORK ON THE STABILITY OF DYNAMICS WITH MULTIPLE TIME DELAYS

多时滞动力学稳定性的创新框架这一SGER提案提出了一个普遍存在但尚未解决的问题：线性时不变多时滞系统（LTI-MTDS）的稳定性评估的创新和独特的视角。它需要一个系统的过程，在时滞域内得到系统稳定性的完整映射。这种范式被称为“特征根的簇处理- ctcr”，它建立在LTI-MTDS的两个非常有趣的特性之上，直到PI最近的工作才认识到这些特性。要求拨款进行为期一年的研究，研究两个关键方向：(a)探讨高阶动态和更多时间延迟的新程序的可行性；(b)引入控制LTI-MTDS的新概念：时间延迟调度（管理）。如果理解得好，这种策略可以为控制设计师引入一个强大的工具。更广泛的影响表现在以下几个方面：科学影响：该研究涵盖了一个非常重要和基础的研究课题。众所周知，TDS在数学上非常具有挑战性。我们建议从现象学的角度，CTCR，来帮助理解它们的稳定性。其次，研究结果的潜在利用潜力很大。同时加工中的机床颤振、数据网络通信和拥塞动态等重要动态都受MTDS的控制。教育影响：PI将进一步从这项研究中获益，将一些研究结果纳入他的高级研究生课程“ME 379控制系统设计进展”。他已经在2003年秋季学期教过这门课教学大纲中有一部分是关于TDS稳定性的。

AN INNOVATIVE FRAMEWORK ON THE STABILITY OF DYNAMICS WITH MULTIPLE TIME DELAYSThis SGER proposal presents an innovative and unique perspective on a ubiquitous yet unsolved problem: the stability assessment of linear time invariant multiple time delay systems (LTI-MTDS). It entails a systematic procedure resulting in a complete map of the system stability in the domain of the time delays. This paradigm called "the cluster treatment of characteristics roots-CTCR" is built upon two very interesting properties of LTI-MTDS which were unrecognized until the recent work of the PI. The funding is requested for a one-year study on two key directions: (a) To explore the viability of the new procedure for higher order dynamics and higher number of time delays, (b) To introduce a new concept of controlling LTI-MTDS: time-delay scheduling (management). If understood well such a strategy can introduce a powerful tool to the controls designer.The broader impact appears in several categories: Scientific impact: The study covers a very important and basic research topic. The TDS are known to be mathematically very challenging. We suggest a phenomenological perspective, CTCR, to help understand their stability properties. Secondly, the potential utilization of the findings is strong. Some important dynamics are governed by MTDS, such as machine tool chatter in simultaneous machining, the data-network communications and congestion dynamics. Educational impact: The PI will further profit from this research by incorporating some of the findings into his advanced level graduate course 'ME 379 Advances in Control System Design". He has taught this course in Fall 2003 semester already and a part of the syllabus was on TDS stability.