Self-organization of spatio-temporal patterns in non-equilibrium systems is a ubiquitous phenomenon that occurs in many areas of science and technology, such as materials science, chemical and biological engineering, nanotechnology, biology and medicine, etc. A new direction of research in this area is the feedback control of pattern-forming systems. The proposed project is devoted to the study of feedback control of pattern-forming systems on the basis of most generic nonlinear evolution equations that can be applied to a large class of various systems in physics, chemistry and biology. Specifically, the research will be focused on the following aspects: (i) feedback control of subcritical instabilities in monotonically and oscillatory unstable systems; (ii) feedback control of selection of stationary and wave patterns; (iii) feedback control of nonlinear dynamics in unstable systems with Goldstone mode; (iv) feedback control of nonlinear dynamics in non-variational systems; (v) feedback control of driven phase-separating systems.
In many areas of science and technology - materials science, chemical and biological engineering, nanotechnology, biology and medicine - self-assembly of regular spatio-temporal patterns and structures is observed. This phenomenon provides an efficient and inexpensive route for creating new types of devices and technologies. It is very important to be able to control self-organization processes in pattern forming systems. A promising way to do that is to apply a feedback control by which the desired structure or behavior is achieved by appropriately adjusting the system parameters in real time according to the observed system characteristics. The proposed project is devoted to the investigation of feedback control of self-organization in most generic pattern-forming systems. The results of this research will therefore be applicable to a large variety of systems in physics, chemistry and biology, and will allow to determine the most efficient ways to control self-assembly processes in many new technologies.