Research On Nonlinear Time-Varying Delay Optimal Control In Microbial Batch Fermentation Of 1,3-Propanediol

1,3-Propanediol(1,3-PD)is an indispensable raw material in chemical production.The production of 1,3-PD by microbial batch fermentation has the advantages of high concentration and simple operation,and has been widely studied at home and abroad.Time delays are common in production processes.At present,time-delay optimal control systems are widely used in the fields of biopharmaceutical,chemical production,multi-agent systems,and so on.In this paper,the optimal control theory and algorithm for a class of nonlinear time-varying time-delay systems are studied based on the background of the 1,3-PD process produced by microbial fermentation in industrial production.Research includes establishing mathematical models,proposing optimal control algorithms with time-varying delays based on optimal control theory,and analyzing and optimizing them.Numerical simulation verifies the feasibility and effectiveness of the proposed algorithm.The research results of this topic have significances for the optimization and control of the 1,3-PD process in microbial batch fermentation,and also provide a reference for the research and application of time-varying delay optimal control systems.The main contents are as follows:1.The single objective time-varying delay optimal control problem in the production of 1,3-PD from glycerol by batch fermentation is studied.In view of the existence of time delays in this process,a nonlinear time-varying delay differential system is proposed to characterize this process.The goal of this paper is to maximize the yield of 1,3-PD at the terminal time.Based on this,a time-varying time-delay optimal control model is established to calculate the optimal initial biomass,initial glycerol,and fermentation duration.In order to transform the optimal control model into an optimization problem with fixed terminal times,a time-scaling transformation technique is proposed.By applying the penalty function method,the corresponding problem is transformed into an optimization problem with only box constraints,and an improved differential evolution algorithm is designed to solve it.Numerical results show that the proposed algorithm has significantly improved compared to existing results.2.The problem of bi-objective time-varying delay optimal control for the production of 1,3-PD from glycerol by batch fermentation is studied.Taking maximizing 1,3-PD yield and minimizing glycerol consumption as objective vector,a bi-objective time-varying delay optimal control model is proposed.The major difference between a bi-objective optimization problem and a single objective optimization problem is that the bi-objective optimization problem is a vector optimization problem.However,there is only a partial order relationship between vectors,making it difficult to directly compare the values of vectors.In this paper,the time-scaling transformation technique and the exact penalty function method are applied to transform the bi-objective time-varying delay optimal control problem into a series of bi-objective optimization problems.The HDE-NSGA-Ⅱ intelligent algorithm is designed to solve the bi-objective optimization problem.Through experimental analysis using multiple classical test functions,the Pareto frontier obtained shows the distribution of the optimal objective value,indicating the effectiveness of the obtained optimal control strategy.