Robust impulsive time-delay optimal control in fed-batch fermentation process
The robust impulsive time-delay optimal control problem in a fed-batch fermentation process is investigated.Firstly,we pro-pose a nonlinear state-dependent impulsive time-delay system to describe the process of fermenting glycerol to produce 1,3-propanediol(1,3-PD)in fed-batch fermentation.Due to the difficulty in accurately estimating the kinetic parameters during the fed-batch fermen-tation process,a robust time-delay optimal control model subject to continuous state inequality constraints is proposed.Here,the objec-tive function is the weighted sum of the terminal concentration of 1,3-PD and its sensitivity with respect to kinetic parameters,and the control vector includes the critical concentration of glycerol and the volume of adding glycerol at each feeding time in the feeding proces-ses.Furthermore,by introducing an auxiliary impulsive system,the robust optimal control problem is transformed into an equivalent standard optimal control problem.By applying the constraint transcription technique,the equivalent optimal control problem is conver-ted into a penalty problem with only box constraints.Finally,a parallel differential evolution algorithm is developed to solve the trans-formed penalty problem.The numerical results indicate that although a small amount of 1,3-PD concentration is sacrificed,the robust-ness of the system is significantly improved when the parameters are subjected to small disturbances.
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