Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study.

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.

Manipulation of surface reaction dynamics by global pressure and local temperature control: a model study.

Specific catalyst design and external manipulation of surface reactions by controlling accessible physical or chemical parameters may be of great benefit for improving catalytic efficiencies and energetics, product yield, and selectivities in the field of heterogeneous catalysis. Studying a realistic spatiotemporal one-dimensional model for CO oxidation on Pt(110) we demonstrate the value and necessity of mathematical modeling and advanced numerical methods for directed external multiparameter control of surface reaction dynamics. At the model stage we show by means of optimal control techniques that species coverages can be adjusted to desired values, aperiodic oscillatory behavior for distinct coupled reaction sites can be synchronized, and overall reaction rates can be optimized by varying the surface temperature in space and time and the CO and O2 gas phase partial pressure with time. The control aims are formulated as objective functionals to be minimized which contain a suitable mathematical formulation for the deviation from the desired system behavior. The control functions pCO(t) (CO partial pressure), pO2(t) (O2 partial pressure), and T(x,t) (surface temperature distribution) are numerically computed by a specially tailored optimal control method based on a direct multiple shooting approach which is suitable to cope with the highly nonlinear unstable mode character of the CO oxidation model.