Robust Control of Constrained Linear Parameter Varying Systems and Applications

线性时不变系统的SznaierRobust控制在过去的二十年里经历了广泛的发展，产生了强大的形式化理论，如H8，u-综合/分析，以及最近的l1最优控制，并成功地应用于具有挑战性的实际问题。相比之下，处理线性参数变化对象的工具才刚刚出现，还远远没有完成。一个悬而未决的问题是对产出和控制行动中的约束的非保守处理，这是许多实际问题的核心。拟议的研究旨在通过将准确处理广泛类别的性能规范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，拟议研究的目标是：o开发一个分析框架，用于合成受硬约束的健壮LPV系统。这个框架应该表现出以下特性：(A)以非保守的方式处理控制和输出约束；(B)确定系统性能的内在极限以及限制因素；以及(C)产生易于计算的过程，从而产生实际可实现的控制器。o将所得到的理论应用于几个跨越广泛应用的问题，例如主动视觉和石油勘探。拟议的研究将结合泛函分析、生存理论和动态系统理论的元素，遵循共同PI在LTI系统中成功地使用的处理约束的方法。初步结果表明，该方法得到了一个具有期望特性的框架，PI期望这一研究工作将导致一个扩展的LPV系统的鲁棒控制框架，能够解决实际问题，既不需要潜在的保守近似，也不需要多次试错型迭代。此外，除了推进控制理论的最先进水平，他预计通过消除目前可用的LPV工具的一些限制，它将促进相关领域的进步。计算机视觉就是一个例子，在这个领域，最近的技术进步使一些实际应用成为可能，前提是某些相关的控制问题可以解决。这些应用范围从智能高速公路系统到远程手术，具有广泛影响社会的潜力。拟议的研究还将直接影响宾夕法尼亚州立大学(PSU)和城市自治大学(UAM)的研究生和本科生教育质量。除了学生直接参与并将结果纳入课程外，UAM的学生还可以使用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获得墨西哥石油学院的专有数据和实验。

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.