SFB 910: Control of Self-Organising Non-Linear Systems: Theoretical Methods and Concepts of Application

SFB 910：自组织非线性系统的控制：理论方法和应用概念

• 批准号: 163436311
• 金额: --
• 依托单位: Freie Universität Berlin
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/163436311?language=en
• 关键词: SFB; 910; Control; Self; Organising

The overarching goal of the Collaborative Research Center (CRC) 910 is to control dissipative structures in nonlinear dynamical systems far from thermodynamic equilibrium. Such systems often exhibit self-organization, i.e., the spontaneous emergence of temporal, spatial, or spatio-temporal structures from the in-herent nonlinear cooperative dynamics. Dissipative structures in self-organizing nonlinear systems are wide-spread in physics, chemistry, and biology.With this CRC we go beyond merely describing the intriguing dynamics of self-organizing nonlinear systems: by combining an interdisciplinary team of applied mathematicians, theoretical physicists, and computational neuroscientists we aim at developing novel theoretical approaches and methods of control, and demonstrating the application of these concepts to a selection of innovative self-organizing systems ranging from condensed hard and soft matter to biological systems. To meet these challenges, we are merging and advancing concepts from the control of nonlinear dynamical systems, the classical mathematical control and optimization theory, and coherent quantum control. Our focus is on theoretical and methodological developments from a conceptu-al point of view (project group A) and with a perspective on applications (project group B). Our key areas of application, which we have already opened up in the first and second funding period, are quantum systems, soft condensed matter, and various types of networks. In the third funding period we will, on the one hand, fur-ther strengthen the synergies and collaborations in and between these fields. On the other hand, we introduce new foci such as control of (classical) multilayer and chemical reaction networks, control of topological quan-tum information processing, mathematical control of stochastic systems, and control of active and turbulent fluids. The application of our concepts to concrete experiments will be fostered by specific external collabora-tions of the individual projects. Depending on the dynamical system considered, its control may target different aspects such as stabilization of unstable steady states, periodic oscillations, or spatio-temporal patterns, suppression of chaos (chaos control), design of the dynamics of a complex network, or control of the coherence and timescales of noise-mediated motion. A particularly important concept in our CRC is feedback control (closed-loop control), where unstable states are stabilized adaptively by using the internal dynamics of the system to adjust the control force, rather than externally imposing a fixed value. A versatile example is provided by time-delayed feedback control, where the control signal is constructed from some time-delayed output variable of the system. Using algo-rithms of optimal control, the proposed control methods can be optimized with respect to the forcing or feed-back protocol in order to minimize, for example, the energy and the time needed to achieve control.

协作研究中心（CRC）910的首要目标是控制远离热力学平衡的非线性动力系统中的耗散结构。这样的系统通常表现出自组织，即，从内在的非线性合作动力学中自发出现的时间、空间或时空结构。自组织非线性系统中的耗散结构在物理学、化学和生物学中广泛传播。通过本CRC，我们不仅仅描述自组织非线性系统的有趣动力学：通过结合应用数学家，理论物理学家和计算神经科学家的跨学科团队，我们旨在开发新的理论方法和控制方法，并展示了这些概念的应用，以选择创新的自组织系统，从凝聚的硬物质和软物质的生物系统。为了应对这些挑战，我们正在融合和推进非线性动力系统控制，经典数学控制和优化理论以及相干量子控制的概念。我们的重点是从概念的角度（项目组A）和应用的角度（项目组B）的理论和方法的发展。我们在第一和第二个资助期已经开放的关键应用领域是量子系统，软凝聚态物质和各种类型的网络。在第三个资助期内，我们一方面会进一步加强这些领域的协同作用和合作。另一方面，我们介绍了新的焦点，如控制（经典）多层和化学反应网络，控制的拓扑量子信息处理，数学控制的随机系统，和控制的活动和湍流流体。我们的概念的具体实验的应用将通过具体的外部合作的个别项目。根据所考虑的动力系统，其控制可以针对不同的方面，例如稳定不稳定的稳态，周期性振荡或时空模式，抑制混沌（混沌控制），设计复杂网络的动力学，或控制噪声介导的运动的相干性和时标。在我们的CRC中一个特别重要的概念是反馈控制（闭环控制），其中不稳定状态是通过使用系统的内部动态来调整控制力而自适应地稳定的，而不是外部强加一个固定值。一个通用的例子是时滞反馈控制，其中控制信号是由系统的一些时滞输出变量构成的。使用最优控制的算法，所提出的控制方法可以相对于强制或反馈协议进行优化，以便最小化例如实现控制所需的能量和时间。