Input-to-state stability and stabilization of distributed parameter systems
分布参数系统的输入状态稳定性和稳定性
基本信息
- 批准号:281417092
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Research Grants
- 财政年份:2015
- 资助国家:德国
- 起止时间:2014-12-31 至 2017-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Robust stability and stabilization of control systems are fundamental and challenging problems in control theory and its applications. One of the milestones of stability theory is the theory of input-to-state stability (ISS), developed over the last two decades for ordinary differential equations and more general finite dimensional systems. This concept is especially useful for the analysis of robust stability of nonlinear systems, control design for nonlinear systems and the dynamics of interconnected systems.However, in the area of infinite-dimensional systems the theory is far from being complete. In modern applications, a crucial role is played by distributed parameter systems (DPS), both linear and nonlinear. ISS theory for such systems is becoming increasingly popular in recent years, but it is still fragmentary and considerably less developed than the finite dimensional case. Furthermore, over the last decade novel methods for stabilization of infinite-dimensional systems have been proposed; most notably, a continuum backstepping method. These approaches yield ISS-based methods for the design of robust and adaptive controllers for linear and nonlinear distributed parameter systems. To obtain powerful methods for control, however, major steps in theunderstanding and development of these methods are still required.In this project we are going to build a firm basis for the investigation of input-to-state stability and stabilization of distributed parameter systems. More specifically, our aims are:1. To develop an ISS theory for linear and bilinear distributed parameter systems, including criteria for input-to-state stability and stabilizability of linear and bilinear DPS and sufficient conditions for robustness of ISS.2. To obtain the infinite-dimensional counterparts of fundamental nonlinear results from ISS theory of finite-dimensional systems. In particular, Lyapunov characterizations of the ISS property, small-gain theorems for DPS and characterizations of ISS in terms of other stability properties.3. To develop methods for robust stabilization of infinite-dimensional systems, namely, a robust version of continuum backstepping, finite-time robust stabilization of partial differential equations and design of ISS stabilizers for port-Hamiltonian systems.In order to obtain these aims expertise is required in ISS theory, functional analysis, semigroup theory, infinite-dimensional systemstheory, partial differential equations, backstepping design and Lyapunov theory. Therefore we will work on this project as a team,consisting of three groups with complementary knowledge covering all of the above topics. It is the aim of the project to establish a solid basis for the long term development of ISS theory as a fundamental tool for a wide range of nonlinear infinite-dimensional systems.
控制系统的稳定稳定性和稳定是控制理论及其应用中的基本和挑战性问题。稳定理论的里程碑之一是在过去的二十年中针对普通微分方程和更一般的有限维度系统开发的投入到国家稳定理论(ISS)。该概念对于分析非线性系统的稳健稳定性,非线性系统的控制设计以及互连系统的动力学特别有用。在现代应用中,线性和非线性的分布式参数系统(DPS)扮演着至关重要的角色。近年来,此类系统的ISS理论越来越流行,但它仍然是零碎的,并且比有限的维度案例要少得多。此外,在过去的十年中,已经提出了无限维系统稳定的新方法。最值得注意的是,连续的后退方法。这些方法产生了基于ISS的方法,用于设计线性和非线性分布式参数系统的鲁棒和自适应控制器。但是,为了获得强大的控制方法,仍然需要进行这些方法的理解和发展的主要步骤。在本项目中,我们将建立一个牢固的基础,以调查输入到州的稳定性和分布式参数系统的稳定。更具体地说,我们的目标是:1。为了开发线性和双线性分布式参数系统的ISS理论,包括针对国家稳定性的标准以及线性和双线性DPS的稳定性以及ISS鲁棒性的足够条件。2。为了获得ISS有限维系统理论的基本非线性结果的无限维度对应物。特别是,lyapunov表征了ISS属性的特征,DPS的小增长定理以及ISS的特征在其他稳定性属性方面。3。为了开发无限二维系统稳定稳定的方法,即,连续性后替代,有限的时间稳定的局部微分方程和ISS稳定器的设计有限的稳定稳定性和设计用于哈米尔顿港系统的稳定剂。在ISS理论,功能分析中,需要获得这些目标,以获得这些目标,分析,分析,分别为差异,分析,分别为差异化,分别为差异。和Lyapunov理论。因此,我们将作为一个团队从事这个项目,由三个群体组成,涵盖了上述所有主题。该项目的目的是建立ISS理论的长期发展作为广泛非线性无限维系统的基本工具的扎实基础。
项目成果
期刊论文数量(5)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Infinite-Dimensional Input-to-State Stability and Orlicz Spaces
- DOI:10.1137/16m1099467
- 发表时间:2016-09
- 期刊:
- 影响因子:0
- 作者:B. Jacob;R. Nabiullin;J. Partington;Felix L. Schwenninger
- 通讯作者:B. Jacob;R. Nabiullin;J. Partington;Felix L. Schwenninger
Characterizations of Input-to-State Stability for Infinite-Dimensional Systems
- DOI:10.1109/tac.2017.2756341
- 发表时间:2017-01
- 期刊:
- 影响因子:6.8
- 作者:A. Mironchenko;Fabian R. Wirth
- 通讯作者:A. Mironchenko;Fabian R. Wirth
Stability conditions for infinite networks of nonlinear systems and their application for stabilization
- DOI:10.1016/j.automatica.2019.108643
- 发表时间:2020-02-01
- 期刊:
- 影响因子:6.4
- 作者:Dashkovskiy, Sergey;Pavlichkov, Svyatoslav
- 通讯作者:Pavlichkov, Svyatoslav
Non-coercive Lyapunov functions for infinite-dimensional systems
无限维系统的非强制 Lyapunov 函数
- DOI:10.1016/j.jde.2018.11.026
- 发表时间:2019
- 期刊:
- 影响因子:2.4
- 作者:A. Mironchenko;F. Wirth
- 通讯作者:F. Wirth
On continuity of solutions for parabolic control systems and input-to-state stability
- DOI:10.1016/j.jde.2018.11.004
- 发表时间:2017-09
- 期刊:
- 影响因子:2.4
- 作者:B. Jacob;Felix L. Schwenninger;H. Zwart
- 通讯作者:B. Jacob;Felix L. Schwenninger;H. Zwart
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Professor Dr. Sergey Dashkovskiy其他文献
Professor Dr. Sergey Dashkovskiy的其他文献
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{{ truncateString('Professor Dr. Sergey Dashkovskiy', 18)}}的其他基金
Stability and robustness of attractors of nonlinear infinite-dimensional systems with respect to disturbances
非线性无限维系统吸引子对扰动的稳定性和鲁棒性
- 批准号:
405685496 - 财政年份:2019
- 资助金额:
-- - 项目类别:
Research Grants
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
- 批准号:
197928859 - 财政年份:2011
- 资助金额:
-- - 项目类别:
Research Grants
Extremum seeking for analog, digital and interconnected systems
极度追求模拟、数字和互连系统
- 批准号:
436509740 - 财政年份:
- 资助金额:
-- - 项目类别:
Research Grants
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