Robust identification of nonlinear state-dependent impulsive switched system with switching duration constraints

In this paper, we will study the problem in fed-batch culture of glycerol producing 1,3-propanediol induced by Klebsiella pneumonia. In practice, the concentrations of intracellular substances are difficult to be measured. To address this problem, quantitative biological robustness is introduced to identify the unknown parameters related to the concentrations of intracellular substances. The problem is formulated as an optimization problem governed by a nonlinear state-dependent impulsive switched (NSDIS) system with unknown switching times and a set of system parameters. The formulated optimization problem is subject to parameter constraints and continuous state inequality constraints. The time scaling transformation, an exact penalty method and binary relaxation approach are introduced to solve the problem. Due to the complexity of the formulated problem, a hybrid parallel algorithm through integrating artificial bee colony algorithm and gradient-based exact penalty approach is proposed. The effectiveness of our proposed method is validated through numerical experiments.