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

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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.