Global Controllability and Stabilization of Bilinear SystemsWith Applications To Large Power Networks

9530917 Mohler这项研究的目的是发展一种新的多维非齐次时不变双线性系统(BLS)的全局能控性和镇定方法，并将其应用于大型输电网络，特别是柔性交流输电系统(FACTS)。对动力系统定性行为的全面理解是研究可控性和稳定性的所有方法的基础。为此，这一建议的基础是由提出者最近引入的一种新的方法来研究BLS的全局定性行为。它的核心是一种非线性分解技术，它将研究转化为对有限数量的相应“基本”不受控系统的定性行为的分析。这项工作假定控制是无界的(否则是有限的)。这一建议的目标之一是改进这一技术，并区分在什么条件下可以通过有界有限控制(这是主要的实际要求)实现目标可控性(在无限时间内)。这里的目的是集中于三维情况，并根据所涉及的矩阵的特征向量和特征函数给出其完整的解。结果表明，该定性法很好地适用于某些由乘子(系数)控制的多维非线性动态系统的分析，其中包括大型输电网络。后一种系统具有很大的实用价值，从世纪之交开始就是无数研究人员和实用工程师深入研究的主题。另一方面，对于本方案的主题，主要考虑了附加阻尼和局部可控性。这项拟议的研究的重点是全局方面的可达性和可控性，以及通过乘数/系数稳定(这些是密切相关的)。这种类型的控制结构是由FACTS等大量自适应系统应用所推动的，它在提高现代电力系统的动态性能方面发挥着重要作用，并可以增加暂态稳定裕度。据我们所知，人们对这项提案所涉及的问题知之甚少。本文提出的研究可以分为两个部分。另一方面，我们从分析开始，利用了传统上认为在一般全球研究中不可避免的无限控制。另一方面，考虑到实际控制通常是有限的，甚至可能是某种符号，我们也为前述的无界控制引入了这些假设。这种方法的思想是，如果全局可控性/可达性/稳定化结果对于无界(但有限，比如说非负)控制成立，那么对于受限能力的真实设备，人们可以预期/证明它在局部方面(不一定很小)是正确的。然而，特别有兴趣的是，根据所提议的方法，区分哪些情况下可以通过有限度的控制来实现全球结果。***

9530917 Mohler The aim of this research is to develop a new global controllability and stabilization methodology for multidimensional nonhomogeneous time-invariant bilinear systems (BLS) with applications to large power transmission networks, particularly Flexible AC Transmission Systems (FACTS). A through understanding of the qualitative behavior of a dynamic system is the foundation of all the methods for controllability and stabilization studies. To this end, the basis for this proposal is formed by a new method recently introduced by the proposers to study the global qualitative behavior of BLS. Its core is a nonlinear decomposition technique converting the study into the analysis of the qualitative behavior of a finite number of the corresponding "basic" uncontrolled systems. The work assumes the unboundedness of (otherwise finite) control. One of the goals of this proposal is to refine this technique and to distinguish the conditions under which the goal controllability can be achieved (in infinite time) by bounded finite controls (which is the main practical requirement). The intent here is to focus on the 3-D case and to give its complete solution in terms of eigenvectors and eigenfunctions of the matrices involved. In turns out that the aforementioned qualitative method fits quite nicely to the analysis of some multidimensional nonlinear dynamic systems controlled via multipliers (coefficients), 9530917 including large power transmission networks. The latter systems are of great practical importance and were the subject of intensive studies for numerous researchers and practical engineers from the turn of the century. On the other hand, in relation to the topic of this proposal, mostly additive damping and local controllability were considered. The emphasis of this proposed research is given to the global aspects of reachability and controllability, and stabilization (these are closely related) via multipliers/coefficients. This type of control structure is motivated by numerous adaptive system applications such as FACTS, which play an important role in enhancing dynamic performance of modern power systems and can increase transient stability margins. To our knowledge, very little is known about the questions which this proposal addresses. The research proposed here can be split into two parts. We start, on the other hand, with the analysis making use of unbounded controls as traditionally assumed unavoidable in general global studies. On the other hand, taking into account that practical controls are normally finite and may be even of a certain sign, we also introduce these assumptions for the aforementioned unbounded controls. The idea of this approach is that if a global controllability/reachability/stabilization result holds for unbounded (but finite, say nonnegative) controls, then one can expect/show it to be true in the local aspect (not necessarily small) for the real device of restricted capability. Yet it is of particular interest, however, to distinguish, based on the proposed methodology, the cases when the global result can be achieved by bounded controls. ***