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

合作研究中心(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。这类系统通常表现出自组织，即从固有的非线性合作动力学中自发地出现时间、空间或时空结构。自组织非线性系统中的耗散结构在物理、化学和生物学中广泛存在。通过这个CRC，我们不仅仅描述了自组织非线性系统的有趣的动力学：通过结合应用数学家、理论物理学家和计算神经学家的跨学科团队，我们的目标是开发新的理论途径和控制方法，并展示这些概念在从凝聚硬物质和软物质到生物系统的一系列创新的自组织系统中的应用。为了迎接这些挑战，我们正在融合和推进来自非线性动力系统控制、经典数学控制和最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)和从应用的角度(项目组B)发展理论和方法。我们的关键应用领域是量子系统、软凝聚物质和各种类型的网络，我们已经在第一个和第二个资助期开辟了这两个领域。在第三个资助期，我们一方面将进一步加强这些领域的协同作用和合作。另一方面，我们还介绍了(经典)多层膜和化学反应网络的控制、拓扑量信息处理的控制、随机系统的数学控制、活性流体和湍流流体的控制等新的研究热点。我们的概念在具体实验中的应用将通过个别项目的具体外部合作来促进。根据所考虑的动力系统的不同，其控制可以针对不同的方面，如不稳定稳态的稳定、周期振荡或时空模式、混沌的抑制(混沌控制)、复杂网络的动力学设计，或者控制噪声介导的运动的相干性和时间尺度。在我们的CRC中，一个特别重要的概念是反馈控制(闭环系统控制)，其中不稳定的状态通过使用系统的内部动态来调整控制力来自适应地稳定，而不是外部施加固定值。时滞反馈控制提供了一个通用的例子，其中控制信号是由系统的某个时滞输出变量构成的。利用最优控制算法，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。

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.