Risk Adjusted Robust Control Theory and Applications

本研究的目的是开发一种全面的风险调整鲁棒控制方法，从使用实验数据获取和验证工厂描述开始，并以具有违反性能规范的规定风险的闭环系统结束。它的概念支柱是算子理论和随机工具的结合，强调计算复杂性和结果的实用性。智力优势：在过去二十年中发展起来的传统鲁棒控制框架已被证明在解决非结构化不确定性系统的鲁棒性和性能问题方面非常成功。在结构不确定性的情况下，在较小程度上也是如此，前提是不确定性块的数量很小，所考虑的工厂具有中等规模，这里的限制因素是所得到的优化问题的计算和缩放特性。另一个限制源于这样一个事实，即这些方法对稳定性和性能都采取了最坏的方法。虽然可以为前者提供一个非常强有力的理由，但在许多情况下，可以针对使用最坏情况方法来提高性能提出一个同样强有力的理由，因为它可能导致系统过于保守。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co pi的初步工作证实），在这种方法中，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）最终控制器的复杂性及其保守性。与目前可用的技术相比，建议的框架提供的优势包括：a。-系统地合成低复杂性、可实际实现的健壮系统。-导致可处理的问题，并且在潜在问题本质上是困难的情况下，提供具有风险调整证书的计算可处理的松弛。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控制器合成，这两者都超出了迄今为止可用方法的能力。-指示设备性能的内在限制，明确不可避免的设计权衡，并允许控制工程师明确地做出这些权衡，而不需要反复试验和错误，当某些要求无法满足时，优雅地降低性能。更广泛的影响：除了推进当前控制理论的艺术状态外，拟议的研究将使目前处于概念验证阶段的几种技术更接近实际。这些例子包括主动视觉应用于感知环境和通信网络，具有改进的业务和服务质量特征。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结果系统缺乏鲁棒性。解决这种脆弱性超出了当前可用的鲁棒控制技术的能力，因为它们的计算和缩放特性很差。教育影响：除了有利于研究生教育外，我们计划将本研究的结果纳入本科鲁棒控制入门课程，这将使学生在早期阶段接触到鲁棒性和计算复杂性的问题。这通常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一些最强大、最发达的资产，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个初步的接触，消除了学生需要等到建立功能分析的背景，以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.