A bilevel approach to biobjective inverse optimal control of nonlinear fermentation system with uncertainties

Abstract

Inverse optimal control is a framework to deal with the optimal control of dynamical systems with uncertain parameters. Bioconversion of glycerol to 1,3-propanediol in continuous fermentation is a complex cellular metabolic process in nature. Due to the unclear metabolic mechanisms and the lack of experimental data of intracellular concentrations, kinetic parameters of the fermentation system are often to a certain degree uncertain. This paper proposes a biobjective inverse optimal control problem with functional inequality constraints to describe the process control of glycerol continuous fermentation system considering the uncertainties of kinetic parameters, where the objectives are formulated based on the biological robustness and the settling time under approximately stable state. A novel distance-based stochastic comparison principle is designed to handle the complex constraints. A bilevel approach using nested strategy is also constructed to solve the biobjective bilevel problem, which is a combination of whale optimization algorithm with the new comparison principle for the lower level and chaotic competitive differential evolution algorithm for the upper level. Numerical comparisons show that the novel comparison principle has certain advantages in convergence speed for 13 benchmark functions compared with two other constraint handling techniques and the obtained optimal dilution rate is effective to avoid glycerol waste for about 30 h. Numerical results show that the proposed bilevel algorithm is effective and practicable to the complex real problem.