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Updated: Aug 15, 2026

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Published on: January 31, 2020
Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model
U Brandt-Pollmann1, D Lebiedz, M Diehl
1Interdisciplinary Center for Scientific Computing, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany.
Abstract:
Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.
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