Risk Adjusted Robust Control Theory and Applications

这项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对象描述开始，以具有违反性能规范的规定风险的闭环系统结束。它的概念基础是算子理论和随机工具的结合，强调结果的计算复杂性和实用性。智能优点：在过去20年中发展的传统鲁棒控制框架被证明在解决非结构化不确定性系统中的鲁棒性和性能问题方面非常成功。在结构不确定的情况下，这在较小程度上也是正确的，假设不确定块的数量很少，所考虑的对象具有中等大小，这里的限制因素是所产生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情况的方法。虽然可以为前者提供非常有力的理由，但在许多情况下，也可以同样有力地反对使用最坏情况方法来提高性能，因为这可能导致系统过于保守。这一提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 PIs的前期工作证实)，在这种方法中，设计者愿意权衡预先分配的违反性能规范的风险，以换取结果控制器的复杂性及其保守性的降低，通常是实质性的。与当前可用的技术相比，所提出的框架提供的优势包括：a.-系统地综合低复杂性、实际可实现的健壮系统。b.-导致容易处理的问题，并且在潜在问题本质上很难的情况下，利用风险调整证书提供计算上容易处理的放松。这些情况的例子包括任意不确定性结构下的模型(In)验证和定阶控制器综合，这两种方法都超出了迄今可用的方法的能力。c.-指示对象性能的内在限制，使不可避免的设计权衡变得清晰，并允许控制工程师明确地进行这些权衡，而不需要反复试验和错误迭代，当某些要求无法实现时，性能会优雅地下降。广泛的影响：除了促进控制理论的最新水平之外，拟议的研究还将使目前处于概念验证阶段的几项技术更接近实用。其中包括主动视觉应用程序，用于感知环境和具有改进的稳健性和服务质量特征的通信网络。可以说，阻碍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健壮性。教育影响：除了使研究生教育受益之外，我们计划将这项研究的结果纳入本科生的稳健控制入门课程，这将使学生在较早的阶段接触到健壮性和计算复杂性问题。这通常是在研究生阶段完成的，因此本科生并不知道这些想法，尽管有人可能会说，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。风险调整后的想法提供了完成这一初始接触的理想工具，消除了等待学生建立解决研究生水平稳健控制课程所需的泛函分析背景的需要。

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.