Optimization of secondary metabolite production using singular approximation and minimum principle

Area of Science:

• Biochemical Engineering
• Process Control
• Mathematical Modeling

Background:

• Optimal control is crucial for maximizing product concentration in bioprocesses.
• Accurate control strategies are needed to approach theoretical maximum yields.
• Existing methods require efficient algorithms for determining optimal control profiles.

Purpose of the Study:

• To compare singular approximation and minimum principle algorithms for optimal control.
• To evaluate the impact of switching points on control profile accuracy.
• To determine the feasibility of achieving near-optimal control with practical approximations.

Main Methods:

• Optimal control profiles were calculated using singular approximation and minimum principle.
• Switching points for singular approximation were determined via mathematical calculation.
• The optimal growth rate was determined using the minimum principle.

Main Results:

• Singular approximation switching points were mathematically determined.
• Optimal growth rate was calculated using the minimum principle.
• Increasing switching points in singular approximation improved profile accuracy towards the minimum principle.
• Three switching times yielded product concentrations approaching 96% of the theoretical optimum.

Conclusions:

• Optimal control can be effectively approximated using methods with multiple switching points.
• Singular approximation with sufficient switching points offers a practical approach to optimal bioprocess control.
• The minimum principle provides a benchmark for theoretical optimal control profiles.