Robust Control of Constrained Linear Parameter Varying Systems and Applications

在过去的二十年里，线性时不变系统的鲁棒控制经历了广泛的发展，导致了强大的形式，如H8， u合成/分析，以及最近的11最优控制，这些形式已经成功地应用于具有挑战性的实际问题。相比之下，用于处理线性参数变化植物的工具刚刚出现，而且还远未完成。一个开放的问题，许多实际问题的中心，是对输出和控制动作的约束的非保守处理。提出的研究旨在通过将精确处理广泛的性能规格和模型不确定性的能力纳入LPV框架来解决这一问题。具体地说，提出的研究目标是：O开发一个分析框架，用于综合受硬约束的鲁棒LPV系统。该框架应表现出下列性质：(a)以非保守方式处理控制和输出限制；(b)查明系统性能的内在限制以及限制因素；(c)产生计算上易于处理的程序，从而产生实际可执行的控制器。O将所得理论应用于主动视觉和石油勘探等广泛应用领域的若干问题。拟议的研究将结合功能分析，可行性理论和动力系统理论的元素，遵循共同pi成功使用的方法来处理LTI系统中的约束。初步结果表明，这种方法可以得到一个具有所需特性的框架。PI期望这项研究工作将为LPV系统提供一个扩展的鲁棒控制框架，能够解决现实问题，既不需要潜在的保守近似，也不需要多次试验和错误类型的迭代。此外，除了提高控制理论的技术水平外，他还希望通过消除当前可用LPV工具的一些限制，促进相关领域的进步。一个例子是计算机视觉，在这个领域，最近的技术进步已经使许多实际应用变得可行，前提是某些相关的控制问题可以得到解决。这些应用范围从智能公路系统到远程手术，具有广泛影响社会的潜力。拟议的研究也将直接影响宾夕法尼亚州立大学（PSU）和大都会自治大学（UAM）的研究生和本科教育质量。除了学生直接参与并将结果纳入课程外，它还将允许UAM的学生使用PSU提供的最先进的计算机视觉设备，而宾夕法尼亚州立大学的学生将受益于访问墨西哥石油研究所的专有数据和实验。

0115946SznaierRobust control of linear time invariant systems has undergone extensive developments in the past two decades, leading to powerful formalisms such as H8, u-synthesis/analysis and, more recently, l1optimal control, that have been successfully applied to challenging practical problems. In contrast, tools for handling linear parameter varying plants have just emerged and are still far from complete. An open issue, central to many practical problems, is the non-conservative handling of constraints, both on the outputs and in the control action. The proposed research is aimed at addressing this issue by incorporating into the LPV frame-work the capability to deal exactly with a broad class of performance specifications and model uncertainty. Specifically, the objectives of the proposed research are:O Development of an analytical framework for synthesizing robust LPV systems subject to hard constraints. This framework should exhibit the following properties:(a) Handle control and output constraints in a non-conservative fashion;(b) Identify the intrinsic limits of performance of the system as well as the limiting factors; and(c) Result in computationally tractable procedures leading to practically implementable controllers.O Application of the resulting theory to several problems spanning a broad spectrum of applications such as active vision and oil prospection.The proposed research will combine elements from functional analysis, viability theory and dynamical systems theory, following an approach successfully used by the co-PIs to handle constraints in the case of LTI systems. Preliminary results indicate that this approach leads to a framework with the desired features.The PI expects that this research effort will result in an expanded robust control framework for LPV systems, capable of addressing realistic problems necessitating neither potentially conservative approximations nor multiple trial and error type iterations. Moreover, in addition to advancing the state of the art in control theory, he expects that by removing some of the limitations of currently available LPV tools, it will foster progress in related areas. An example is computer vision, an area where recent technological advances have rendered a number of practical applications feasible, provided that certain related control issues can be resolved. These applications range from intelligent highway systems to remote surgery and have the potential to broadly impact society.The proposed research will also have a direct bearing upon the quality of graduate and undergraduate education both at Penn State University (PSU) and the Universidad Autonoma Metropolitana (UAM). In addition to direct student involvement and incorporation of the results into the curriculum, it will allow students from the UAM to use state-of-the-art computer vision equipment available at PSU, while Penn State students will benefit from having access to proprietary data and experiments from the Mexican Petroleum Institute.