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Recursive designs of robust and adaptive controllers for extensions of existing canonical forms and for their interconnections

用于扩展现有规范形式及其互连的鲁棒自适应控制器的递归设计

基本信息

批准号：
197928859
负责人：
Professor Dr. Sergey Dashkovskiy
金额：
--
依托单位：
Lehrstuhl für Mathematik II (Dynamische Systeme und Kontrolltheorie)
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2011
资助国家：
德国
起止时间：
2010-12-31 至 2013-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/197928859?language=en
关键词：
Recursive designs robust adaptive controllers

项目摘要

Nonlinear systems appear in many modern engineering problems. Stability is one of the fundamental properties of such systems needed for their performance. Another challenging aspect is the robustness with respect to disturbances that can destabilize them. Furthermore, some parameters of a system can be unknown that leads to various adaptive control problems. During the last two decades such recursive designs as backstepping and forwarding became classical and found many applications in various industrial and engineering problems. However all this classical theory is applicable to some special canonical forms only: strict-feedback or purefeedback in the regular case (feedback linearizable systems), or to their very special polynomial extensions. The goals of the project are: 1) To extend as wide as possible the existing classes of systems the backstepping framework is applicable to and to extend the methods for solving robust and adaptive control problems for these new classes. First, this will be done for ODE systems, then for a wider classes such as delay systems, switched systems (and other types of hybrid systems). 2) To provide constructive algorithms that solve the above-mentioned problems numerically and which suit for the singular case (for systems that do not have a controllable linearization and are not feedback linearizable). 3) As we will work with time-varying systems and use the ISS framework to cope with disturbances, another goal is to extend the ISS theory that exists for time-varying systems to the case of time-varying ones and to use it for the achievement of the first two goals.

非线性系统出现在许多现代工程问题中。稳定性是这类系统的基本性能之一。另一个具有挑战性的方面是相对于可能使其不稳定的干扰的鲁棒性。此外，系统的某些参数可能是未知的，这导致各种自适应控制问题。在过去的二十年中，诸如backstepping和forwarding之类的递归设计成为经典，并在各种工业和工程问题中找到了许多应用。然而，所有这些经典的理论是适用于一些特殊的标准形式：严格反馈或purefeedback在正常情况下（反馈线性化系统），或其非常特殊的多项式扩展。该项目的目标是：1）尽可能广泛地扩展现有的系统类的backstepping框架是适用于和扩展的方法来解决这些新的类的鲁棒和自适应控制问题。首先，这将是为ODE系统，然后为更广泛的类别，如延迟系统，切换系统（和其他类型的混合系统）。2)为了提供建设性的算法，解决上述问题的数字和适用于奇异的情况下（对于系统，没有一个可控的线性化和不反馈线性化）。3)由于我们将处理时变系统并使用ISS框架来科普干扰，另一个目标是将时变系统的ISS理论扩展到时变系统的情况，并使用它来实现前两个目标。