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

• Subject Area: Physics ; Mathematics
• Term: from 2011 to 2022
• Website: Homepage
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 163436311

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.

• DFG Programme: Collaborative Research Centres

Completed projects

• A01 - Control and dynamics of multilayer networks (Project Heads Mandel-Zakharova, Ph.D., Anna ;  Schöll, Eckehard )
• A02 - Analysis and computation of stability exponents for port-Hamiltonian delay differential-algebraic equations (Project Heads Mehrmann, Volker ;  Stykel, Tatjana )
• A03 - Self-organization and control in coupled networks and time-delayed systems (Project Heads Wolfrum, Matthias ;  Yanchuk, Serhiy )
• A04 - Spatio-temporal patterns: control, delays, and design (Project Heads Fiedler, Bernold ;  Schneider, Isabelle )
• A05 - Pattern formation in coupled parabolic systems (Project Head Mielke, Alexander )
• A06 - Control of self-organization in dynamical networks (Project Head Mikhailov, Alexander S. )
• A07 - Feedback control of coherent and collective quantum processes (Project Heads Brandes, Tobias ;  Emary, Clive ;  Schaller, Gernot )
• A08 - Nonlinear evolution equations: model hierarchies and complex fluids (Project Head Emmrich, Etienne )
• A09 - Reaction-diffusion systems: hysteresis and nonlocal interactions (Project Head Gurevich, Ph.D., Pavel )
• A10 - Control of stochastic mean-field equations with applications to brain networks (Project Head Stannat, Wilhelm )
• A11 - Feedback control for quantum information processing (Project Head von Oppen, Felix )
• A12 - Feedback control of atomic quantum gases (Project Heads Eckardt, André ;  Wu, Ling-Na )
• B01 - Feedback control of open quantum networks (Project Heads Carmele, Alexander ;  Knorr, Andreas )
• B02 - Control of dynamical structures and transport in driven colloidal systems (Project Head Klapp, Sabine )
• B04 - Control of flow patterns in complex fluids on the micron scale (Project Head Stark, Holger )
• B05 - Control of multiscale patterns formation and application to cardiac dynamics and active matter (Project Head Bär, Markus )
• B06 - Control of travelling and rotating waves in spatially extended nonlinear systems (Project Heads Engel, Harald ;  Tröltzsch, Fredi )
• B07 - Controlling neural wave dynamics by nonlocal and time-delayed feedback (Project Heads Dahlem, Markus A. ;  Schöll, Eckehard )
• B08 - Dynamics and control of inter-areal brain networks (Project Head Obermayer, Klaus )
• B09 - Stochastic and structural properties of complex laser networks for optical computing (Project Head Lüdge, Kathy )
• B10 - Control of networks with time-varying topologies and applications to epidemiology (Project Head Hövel, Philipp )
• B12 - Control and feedback protocols via dissipation engineering (Project Head Metelmann, Anja )
• MGK - Integrated research training group: design and control of complex systems (Project Heads Carmele, Alexander ;  Mielke, Alexander ;  Stark, Holger )
• Z - Administrative project (Project Heads Klapp, Sabine ;  Schöll, Eckehard )

• Applicant Institution: Technische Universität Berlin
• Participating University: Freie Universität Berlin; Humboldt-Universität zu Berlin; Saratov State University, until 3/2022
• Participating Institution: Physikalisch-Technische Bundesanstalt (PTB); Standort Berlin; Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS); Leibniz-Institut im Forschungsverbund Berlin e. V.
• Partner Organisation: Russian Foundation for Basic Research, until 3/2022
• Spokespersons: Professorin Dr. Sabine Klapp, since 2/2018; Professor Dr. Eckehard Schöll, until 2/2018