DFG Collaborative Research Center 910 on
Control of self-organizing nonlinear systems

Special measures project

Delayed feedback: noninvasive and global control

Research director

Dr. Isabelle Schneider

Members

Alejandro López

David Hering (TU Berlin)

Summary

We investigate two complementary approaches to delayed feedback control: Noninvasive control and global control. On the one hand, we study noninvasive control as inspired by Pyragas, but going far beyond the scope of his original control scheme. In particular, we will address control schemes which include symmetries of the system and new state-dependent control schemes. On the other hand, we introduce the ambitious new concept of global control, which targets the global nonlinear dynamics, rather than just local linear in-/stability. Both settings aim at novel and broadly applicable principles of delayed feedback control.

Preprints and Publications

B. Fiedler, I. Schneider

Stabilized rapid oscillations in a delay equation: Feedback control by a small resonant delay.
in press, Discrete and Continuous Dynamical Systems - Series S (2018).
(pdf, 2.310 kB)
arxiv.org/abs/1708.08101

Alejandro López Nieto

Heteroclinic connections in delay equations
Master Thesis, Freie Universität Berlin, 2017.
(PDF)

A. Röhm, K. Lüdge, I. Schneider

Bistability in Two Simple Symmetrically Coupled Oscillators with Symmetry-broken Amplitude-and Phase-Locking
Chaos: An Interdisciplinary Journal of Nonlinear Science 28 (6) , 063114 (2018)
arxiv.org/abs/1712.01610

Isabelle Schneider

An introduction to the control triple method for partial differential equations
Patterns of Dynamics (Gurevich, Hell, Sandstede, Scheel, eds.), Springer Proceedings in Mathematics & Statistics Volume 205 (2018).
(pdf, 577 kB)