Solving Large Sum-of-Squares Optimization Problems in Control by Exploiting the Parallel Structure of Polya's Algorithm

利用Polya算法的并行结构解决控制中的大平方和优化问题

• 批准号: 1100376
• 负责人: Matthew Peet
• 金额: $ 23.75万
• 依托单位: Illinois Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2012-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1100376&HistoricalAwards=false
• 关键词: Solving; Large; Sum; Squares; Optimization

The goal of this project is to develop new parallel algorithms for control of nonlinear and uncertain systems. Computer architectures are changing, with multi-core chips and graphics cards replacing the CPU-based desktop powerhouses of years past. And with this change, a great deal of control systems technology is becoming obsolete. The problem is that the optimization algorithms being used by controls engineers are not built for the parallel processing environments we are encountering today. Increasingly, this will limit our ability to control the large and complex models we use to describe such phenomena as fusion energy and biological immunity. For this project, we have identified an approach to control of nonlinear or uncertain dynamics based on optimization using Polya's lemma. The unique feature of this approach is that the optimization algorithms when applied to Polya's lemma become almost perfectly parallel. This means that the algorithms we develop can run on almost any type of parallel computing architecture, including cluster computers and supercomputers. Considering that the computing power available on these platforms is currently more than 2,000,000 times great than that available on a single-core desktop, the result of this project will be an order of magnitude increase in the complexity of systems we can control. The project organization has three parts. i) develop parallel algorithms to formulate robust control problems on the simplex as semidefinite-programming problems via Polya's lemma ii) develop parallel primal-dual interior-point algorithms for the problem of robust control on cluster computing and multi-core architectures. Iii) expand the scope beyond robust control to nonlinear analysis and more general types of system uncertainty and include additional computing platforms such as GPU computing and supercomputing. The algorithms developed in this project will be posted online for free distribution using a public license.An order-of-magnitude increase in the complexity of systems that can be controled has important implications. For example, although detailed models of plasma in fusion reactors are available, those models are too complex to control efficiently using existing algorithms. The result is poor plasma confinement and inefficient energy production. If more detailed models can be used to improve plasma confinement, this has far-reaching implications for energy production. Additionally, biological models of interaction between cells in the immune system contain many different actors and are nonlinear and highly uncertain. An improved ability to analyze and control these models may lead to innovative forms of treatment for diseases such as cancer which is believed to be caused by a failure of the immune system to self-regulate. The PI has ongoing projects in both the areas of fusion research and immunology and this research will be integrated into these projects. Finally, this project has an international component with the University of Campinas in Brasil, including extended teaching exchanges in both Campinas and Chicago. This will strengthen the collaborative relationship between these two institutions and provide an international perspective and educational opportunity for students at both schools.

该项目的目的是开发新的并行算法来控制非线性和不确定系统。计算机体系结构正在发生变化，多核芯片和图形卡取代了几年过去几年的基于CPU的台面发电厂。随着这一变化，大量的控制系统技术变得过时了。问题在于，控制器工程师使用的优化算法不是为我们今天遇到的并行处理环境而构建的。 越来越多地，这将限制我们控制我们用来描述融合能量和生物免疫力等现象的大型和复杂模型的能力。 对于这个项目，我们已经确定了一种基于Polya的引理基于优化的非线性或不确定动力学控制的方法。 这种方法的独特特征是，应用于Polya的引理时的优化算法几乎完全平行。这意味着我们开发的算法几乎可以在任何类型的并行计算体系结构上运行，包括群集计算机和超级计算机。考虑到这些平台上可用的计算能力目前比单核桌面上可用的计算能力大于2,000,000倍，因此该项目的结果将是我们可以控制的系统复杂性的数量级。项目组织有三个部分。 i）开发平行算法以通过Polya的引理ii）作为半芬矿编程问题来制定可靠的控制问题，ii）开发出平行的原始偶对偶内点算法，以解决群集计算和多核体系结构的强大控制问题。 iii）将范围扩展到非线性分析和系统不确定性的更多一般类型的范围，并包括其他计算平台，例如GPU计算和超级计算。该项目中开发的算法将在线发布以免费分发使用公共许可证。可以控制的系统的复杂性增加具有重要意义。例如，尽管可以使用融合反应器中的血浆详细模型，但这些模型太复杂了，无法使用现有算法有效地控制。结果是血浆限制和能源产生效率低下。如果可以使用更详细的模型来改善血浆限制，那么这对能源生产具有深远的影响。此外，免疫系统中细胞之间相互作用的生物学模型包含许多不同的参与者，并且是非线性和高度不确定的。分析和控制这些模型的提高能力可能会导致诸如癌症等疾病的创新形式的治疗形式，这被认为是由于免疫系统无法自我调节引起的。 PI在融合研究和免疫学领域都有正在进行的项目，该研究将融入这些项目。最后，该项目与巴西坎皮纳斯大学（Campinas of Brasil）有了国际组成部分，包括坎皮纳斯（Campinas）和芝加哥（Campinas）和芝加哥的扩展教学交流。这将加强这两个机构之间的协作关系，并为两所学校的学生提供国际观点和教育机会。