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General Research Programme

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 inherent nonlinear cooperative dynamics. Dissipative structures in self-organizing nonlinear systems are widespread 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 conceptual 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, further 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 quantum 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 collaborations 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 algorithms of optimal control, the proposed control methods can be optimized with respect to the forcing or feedback protocol in order to minimize, for example, the energy and the time needed to achieve control. A new issue in the third funding period will be optimal control of stochastic mean-field systems and of reaction-diffusion systems for brain networks.

With research on quantum systems, soft condensed matter and networks we continue to study emerging fields of applications for control algorithms which have hitherto been mainly confined to classical macroscopic systems. In the third funding period, new aspects in the field of networks will be multilayer network models, power grids, and quantitative approaches to the reservoir computing performance of optical networks. For quantum systems, a key challenge is to apply concepts of time-delayed feedback to control nonlinear phenomena dominated by quantum fluctuations. In the third funding period we will particularly focus on error corrections for quantum information processing, dissipation engineering and on steering quantum interferences via a coherent self-feedback mechanism beyond classical Pyragas control. Control of soft condensed matter in nonequilibrium such as driven colloidal suspensions and flowing complex fluids is still a novel and innovative issue, challenges being the manipulation of dynamical structures and transport on the particle scale, and the design of microfluidic patterns. New topics here are the control of active fluids, which are intrinsically out of equilibrium, the dynamics under time-delayed feedback, and the control of elastic turbulence. Further we will intensify research on the control of cardiac tissue, an active medium with typically chaotic spatiotemporal dynamics, and on neural systems, where inherent time-delayed and nonlocal feedbacks play an important role. Understanding and designing corresponding control mechanisms may eventually lead to substantial progress in defibrillation and the understanding of the impact of non-invasive brain stimulation on global brain activity.

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