Risk Adjusted Robust Control Theory and Applications

本研究的目的是开发一个全面的方法，风险调整的鲁棒控制，开始使用实验数据，以获得和验证植物的描述和结束与闭环系统，具有规定的风险违反性能指标。它的概念骨干是一个运营商的理论和随机工具，强调计算的复杂性和实用性的结果相结合。智力优点：在过去的二十年中开发的传统的鲁棒控制框架hasproved是非常成功的解决系统的鲁棒性和性能问题受到unstructureduncertainty。这也是真的，在较小的程度上，在结构化的不确定性的情况下，只要不确定性块的数量是小的，所考虑的工厂具有中等规模，这里的限制因素是所产生的优化问题的计算和缩放属性。另外的限制源于这样一个事实，即这些方法采取最坏情况下的方法来稳定性和性能。虽然前者的理由非常充分，但在许多情况下，也可以同样充分地反对使用最坏情况下的性能方法，因为它可能导致过于保守的系统。该建议的动机是通过使用风险调整方法来解决这些问题的可能性（由合作伙伴的后续工作证实），其中设计师愿意权衡预先分配的违反性能规范的风险，以换取减少，通常是实质性的，由此产生的控制器的复杂性及其保守性。所提出的框架相对于当前可用的技术提供的优点包括以下能力：系统地综合低复杂性、实际可实现的鲁棒系统。导致易处理的问题，并在潜在的问题是本质上很难的情况下，提供计算易处理的放松与风险调整证书。这些情况的例子包括任意不确定性结构下的模型验证和固定阶的模糊综合，这两种方法都超出了迄今为止可用的方法的能力。消除工厂性能的固有限制，明确不可避免的设计权衡，并允许控制工程师明确做出这些权衡，而无需反复试验，在某些要求无法满足时优雅地降低性能。除了推进当前控制理论的最新发展，拟议的研究将使目前处于概念验证阶段的几项技术更接近实用。这些例子包括主动视觉应用到感知环境和通信网络，具有改进的鲁棒性和服务质量特性。可以说，阻止这些技术在受控实验室环境之外部署的关键因素之一是缺乏系统的鲁棒性。解决这种脆弱性是超出了目前可用的鲁棒控制technologesdue到他们的计算和缩放properties.Educational影响的能力：除了有利于研究生教育，我们计划将本研究的结果在本科生介绍鲁棒控制课程，这将暴露学生在早期阶段的鲁棒性和计算复杂性的问题。通常这是在研究生阶段完成的，因此本科生不知道这些想法，尽管可以说它们是我们社区拥有的最强大和最好的资产，具有超越纯粹控制的潜力。风险调整的想法提供了一个理想的工具来完成这一初步的曝光，消除了需要等待，直到学生建立的背景功能分析需要解决研究生水平的鲁棒控制课程。

The objective of this research is to develop a comprehensive approach to risk adjusted robust control,starting with the use of experimental data to obtain and validate a plant description and ending with a closedloop system that has a prescribed risk of violating the performance specifications. Its conceptual backboneis a combination of operator theoretic and stochastic tools that emphasizes both computational complexityand practicality of the results.Intellectual Merit: The conventional robust control framework developed in the past two decades hasproved to be very successful in addressing robustness and performance issues in systems subject to unstructureduncertainty. This is also true, to a lesser extent, in the case of structured uncertainty, providedthat the number of uncertainty blocks is small and the plant under consideration has moderate size, with thelimiting factor here being the computational and scaling properties of the resulting optimization problems.An additional limitation stems from the fact that these approaches take a worst case approach both to stabilityand performance. While a very strong case can be made for the former, in many cases an equallystrong case can be made against the use of a worst case approach to performance, since it can lead to overlyconservative systems. This proposal is motivated by the possibility (substantiated by the co PIs preliminarywork) of addressing these issues through the use of a risk adjusted approach, where the designer is willingto trade off a preassigned risk of violating a performance specification in return for a reduction, oftensubstantial, in both the complexity of the resulting controller and its conservatism. Advantages offered bythe proposed framework over currently available techniques include the abilities to:a.- Systematically synthesize low complexity, practically implementable robust systems.b.- Lead to tractable problems, and in cases where the underlying problem is intrinsically hard, toprovide for computationally tractable relaxations with risk adjusted certificates. Examples of thesecases include model (in)validation under arbitrary uncertainty structures and fixer order controllersynthesis, both beyond the ability of hitherto available methods.c.- Indicate the intrinsic limits of performance of the plant, making unavoidable design tradeoffs clearand allowing the control engineer to explicitly make these tradeoffs, without trial and error iterations,gracefully degrading performance when some of the requirements cannot be met.Broader Impact: In addition to advancing the current state of the art in control theory, the proposed researchwill bring closer to being practical several technologies currently at the proof of concept stage. Examplesof these include active vision applications to aware environments and communication networks with improvedrobustness and quality of service characteristics. Arguably one of the critical factors preventing thedeployment of these technologies beyond controlled lab environments is the lack of robustness of the resultingsystems. Addressing this fragility is beyond the ability of currently available robust control techniquesdue to their poor computational and scaling properties.Educational Impact: In addition to benefiting graduate education, we plan to incorporate results from thisresearch in an undergraduate introductory robust control course, that will expose students at an earlier stageto the issues of robustness and computational complexity. Typically this is done at the graduate level, andthus undergraduate students are unaware of these ideas, although it could be argued that they are some ofmost powerful and better developed assets that our community has, with a potential that extend beyondpure control. Risk adjusted ideas provide an ideal vehicle to accomplish this initial exposure, eliminatingthe need to wait until students build the background in functional analysis required to tackle graduate levelrobust control courses.