This paper considers a dynamic optimization problem(DOP)of 1,3-propanediol fermentation process(1,3-PFP).Our main contributions are as follows.Firstly,the DOP of 1,3-PFP is modeled as an optimal control problem of swi...This paper considers a dynamic optimization problem(DOP)of 1,3-propanediol fermentation process(1,3-PFP).Our main contributions are as follows.Firstly,the DOP of 1,3-PFP is modeled as an optimal control problem of switched dynamical systems.Unlike the existing switched dynamical system optimal control problem,the state-dependent switching method is applied to design the switching rule.Then,in order to obtain the numerical solution,by introducing a discrete-valued function and using a relaxation technique,this problem is transformed into a nonlinear parameter optimization problem(NPOP).Although the gradient-based algorithm is very efficient for solving NPOPs,the existing algorithm is always trapped in a local minimum for such problems with multiple local minima.Next,in order to overcome this challenge,a gradient-based random search algorithm(GRSA)is proposed based on an improved gradient-based algorithm(IGA)and a novel random search algorithm(NRSA),which cannot usually be trapped in a local minimum.The convergence results are also established,and show that the GRSA is globally convergent.Finally,a DOP of 1,3-PFP is provided to illustrate the effectiveness of the GRSA proposed by this paper.展开更多
基金the National Natural Science Foundation of China(61963010 and 61563011)the special project for cultivation of new academic talent and innovation exploration of Guizhou Normal University in 2019(11904-0520077)。
文摘This paper considers a dynamic optimization problem(DOP)of 1,3-propanediol fermentation process(1,3-PFP).Our main contributions are as follows.Firstly,the DOP of 1,3-PFP is modeled as an optimal control problem of switched dynamical systems.Unlike the existing switched dynamical system optimal control problem,the state-dependent switching method is applied to design the switching rule.Then,in order to obtain the numerical solution,by introducing a discrete-valued function and using a relaxation technique,this problem is transformed into a nonlinear parameter optimization problem(NPOP).Although the gradient-based algorithm is very efficient for solving NPOPs,the existing algorithm is always trapped in a local minimum for such problems with multiple local minima.Next,in order to overcome this challenge,a gradient-based random search algorithm(GRSA)is proposed based on an improved gradient-based algorithm(IGA)and a novel random search algorithm(NRSA),which cannot usually be trapped in a local minimum.The convergence results are also established,and show that the GRSA is globally convergent.Finally,a DOP of 1,3-PFP is provided to illustrate the effectiveness of the GRSA proposed by this paper.
