Theoretical Development of Passivity-Preserving Variational Balanced Truncation of Linear Systems

摘要：payam heydari，加州大学欧文分校该项目的主要目标是在元素受统计变化影响的线性时不变（LTI）系统的截断平衡实现领域开发一个整合研究和教育的跨学科项目。该提案的研究目标是扩展无源保持平衡截断方法，以考虑系统元素的统计变化。为了减少在感兴趣的频率范围内的误差，PI在频谱加权平衡截断方面的早期工作也可以与所提出的变分技术相结合，以提高所提出方法在感兴趣的频率范围内的准确性。提议的活动将在几个重要的方向上使用平衡截断来扩展LTI系统的模型阶降的能力，例如保证无源性和考虑系统元素的统计变化。与传统的平衡截断方法类似，该算法为降阶系统提供了可证明的误差界。将所提出的变分平衡截断方法与电路级仿真算法相结合，将为电路和系统设计人员提供强大而有效的分析工具，以比蒙特卡罗仿真快几个数量级的速度模拟和优化大型电路，同时保持准确性。提出的研究解决了线性系统理论中的一些基本计算方法，并在许多工程领域应用，特别是电子设计自动化。因此，跨学科的研究和教育，以及政府和行业，将从拟议的工作中受益。PI与当地工业的密切合作将促进研究成果向美国高科技公司传播，为大型统计变化线性系统的新设计工具和方法的开发做出贡献。在考虑新出现的过程可变性问题的同时，模拟大型电路的能力将使以更高的精度进行统计模拟成为可能，这是目前不可能实现的能力。这反过来又会对未来无线/有线系统物理层中使用的多媒体集成电路产生影响。拟议的教育计划将强调在电路分析和优化领域的综合研究和培训计划中，高中，本科和研究生水平的代表性不足的群体的参与。它将促进当地高中的少数族裔学生与加州大学欧文分校的科学家、教育工作者和工程师之间的长期学术关系。

ABSTRACT0514887Payam HeydariUniversity of California - IrvineThe main of objective of this project is to develop an interdisciplinary program integrating research and education in the area of truncated balanced realization for linear time-invariant (LTI) systems whoseelements are subject to statistical variations. The proposal's research objective is to extend the passivity preserving balanced truncation method to account for the statistical variations of system elements. Inan attempt to reduce the error over the frequency range of interest, the PI's earlier work on spectrally-weighted balanced truncation can also be combined with the proposed variational technique to increase the accuracy of the proposed method across the frequency range of interest. The proposed activity will extend the capabilities of the model-order reduction of LTI systems using balanced truncation in severalsignificant directions, such as guaranteeing passivity and accounting for the statistical variation of the system's elements. Similar to conventional balanced truncation methods, the proposed algorithm providea provable error-bound for the reduced-order system. Integrating the proposed variational balanced truncation method with circuit-level simulation algorithms will provide circuit and system designers apowerful and efficient analytical tool to simulate and optimize large circuits orders of magnitude faster than the Monte-carlo simulation, while retaining the accuracy. The proposed research addresses some ofthe fundamental computational approaches in linear system theory with an application in many areas of engineering, particularly electronic design automation. As a consequence, the interdisciplinary research andeducation, as well as government and industry, will benefit from the proposed work. The PI's close collaboration with local industry will facilitate the dissemination of research results to U.S. high-techcompanies to contribute to the development of new design tools and methodologies for large statistically-varying linear systems. The capability of simulating large circuits while accounting for theemerging problem of process variability will make it possible to carry out statistical simulation with far better accuracy, a capability that is currently impossible to achieve. This in turn will have an impact onfuture multimedia integrated circuits used in the physical layer of wireless/wireline systems. The proposed educational plan will emphasize the participation of underrepresented groups at the high school,undergraduate, and graduate levels in the integrated research and training programs in the area of circuit analysis and optimization. It will foster long-term academic relationships between ethnic-minoritystudent populations at local high schools, and the scientists, educators, and engineers at the UC-Irvine.