Computation of impulsive optimal control for 1,3-PD fed-batch culture

• We consider an impulsive optimal control of fed-batch culture.
• A continuous state constrained optimal control problem is then presented.
• We use penalty function and barrier function method.
• A hybrid algorithm by integrating a particle swarm optimization with gradient-based optimization algorithm is proposed.

In this paper, in consideration of suddenly increasing of the glycerol and alkali, we propose a nonlinear impulsive system to describe the fed-batch culture of glycerol bioconversion to 1,3-propanediol (1,3-PD) induced by Klebsiella pneumonia (K. pneumonia). To maximize the concentration of 1,3-PD at the terminal time, we present an impulsive optimal control problem in which the final 1,3-PD yield is taken as the cost function, while the feeding volumes of glycerol and the feeding time points are taken as decision variables. Continuous state inequality constraints are imposed to ensure that the concentrations of biomass, glycerol, and reaction products lie within specified limits. We use the time scaling method to handle the variable feeding time points. The impulsive optimal control problem is approximated as a sequence of nonlinear optimization sub-problems through the application of the penalty function and barrier function method. A hybrid algorithm by integrating a particle swarm optimization with gradient-based optimization algorithm is proposed to seek the optimal feeding strategy. From extensive simulation study, it is observed that the obtained optimal strategy is highly satisfactory.