A new filled function method for global optimization

Gao, Yuelin; Yang, Yongjian; You, Mi

doi:10.1016/j.amc.2015.06.090

Cited by 6 publications

(2 citation statements)

References 18 publications

(16 reference statements)

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“…However, the traditional filled function methods are often non-differentiable and sensitive to some adjustable parameters, or contain ill-conditioned terms and more than one adjustable parameter needing to be controlled [35]. To overcome these limitations, a new filled function method is proposed in [34].…”

Section: A Parallel Filled Function Algorithmmentioning

confidence: 99%

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Optimal control of a batch fermentation process with nonlinear time-delay and free terminal time and cost sensitivity constraint

Yuan

Liu

Zhang

et al. 2016

Journal of Process Control

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In this paper, we consider a nonlinear time-delay dynamic system with uncertain system parameters to characterize the process of batch fermentation. Our goal is to design an optimal control scheme to maximize the productivity of 1,3-propanediol (1,3-PD). Accordingly, we introduce an optimal control problem governed by the nonlinear time-delay dynamic system, in which the control variables are the free terminal time of the batch fermentation process and the initial concentrations of biomass and glycerol. The optimal control problem is subject to a cost sensitivity constraint for ensuring that an acceptable level of the system performance is achieved and continuous state inequality constraints for ensuring that the concentrations of biomass, glycerol, 1,3-PD, acetate, ethanol lie within specified limits. Then, the optimal control problem with free terminal time is transformed, via a hybrid time-scaling strategy, into an equivalent problem with fixed terminal time, which is much preferred for numerical computation. Using the constraint transcription and local smoothing approximation techniques, we approximate these continuous state inequality constraints by conventional inequality constraints to yield an approximate optimal control problem. Because of the highly complex nature of this approximate problem, a parallel algorithm based on the filled function method is constructed to solve this approximate problem. Finally, it is observed that the optimal control obtained is satisfactory through numerical simulations.

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Section: A Parallel Filled Function Algorithmmentioning

confidence: 99%

“…The deviation between the best fitness of current iteration and that of the Kth previous iteration is less thanǫ. [34] that the value of A should be selected large enough and the value of δ should be selected small enough. Otherwise, there could be no minimizer of FF u k p ,A,δ (u) in a better basin.…”

Section: Remark 1 In Step 22 Andmentioning

confidence: 99%