Optimal parameter selection for nonlinear multistage systems with time-delays

Liu, Chongyang; Loxton, Ryan; Teo, Kok Lay

doi:10.1007/s10589-013-9632-x

Cited by 25 publications

(15 citation statements)

References 37 publications

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“…Here, κ 2 = 1 and κ 3 = κ 4 = κ 5 = 3, while Δ l , α l , x * l , ν l , z l , and c 1 , c 2 , c 3 , and c 4 are model constants. The problem of determining optimal estimates for these constants is considered in [38].…”

Section: 3-propanediol Productionmentioning

confidence: 99%

Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

Lin

Loxton

Teo

2013

J. Oper. Res. Soc. China

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A switched system is a dynamic system that operates by switching between different subsystems or modes. Such systems exhibit both continuous and discrete characteristics-a dual nature that makes designing effective control policies a challenging task. The purpose of this paper is to review some of the latest computational techniques for generating optimal control laws for switched systems with nonlinear dynamics and continuous inequality constraints. We discuss computational strategies for optimizing both the times at which a switched system switches from one mode to another (the so-called switching times) and the sequence in which a switched system operates its various possible modes (the so-called switching sequence). These strategies involve novel combinations of the control parameterization method, the timescaling transformation, and bilevel programming and binary relaxation techniques. We conclude the paper by discussing a number of switched system optimal control models arising in practical applications.

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Section: 3-propanediol Productionmentioning

confidence: 99%

Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

Lin

Loxton

Teo

2013

J. Oper. Res. Soc. China

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“…Let ϕ(·|u, τ, α) be the unique continuous solution of the auxiliary time-delay system (15) corresponding to the admissible control pair (u, τ ) ∈ U × Γ and the nominal time-delay α. It can be shown (see, for example [40,41]) that the state x(t|u, τ, α) is differentiable with respect to α and…”

Section: Computing Sensitivitymentioning

confidence: 99%

Robust multi-objective optimal switching control arising in 1,3-propanediol microbial fed-batch process

Liu

Gong

Teo

et al. 2017

Nonlinear Analysis: Hybrid Systems

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This paper considers optimal control of glycerol producing 1,3-propanediol (1,3-PD) via microbial fed-batch fermentation. The fed-batch process is formulated as a nonlinear switched time-delay system. In general, the time-delay in the fed-batch process cannot be exactly estimated. Our goal is to design an optimal switching control scheme to simultaneously maximize 1,3-PD productivity and 1,3-PD yield under time-delay uncertainty. Accordingly, we propose a robust multi-objective optimal switching control model, in which two objectives, i.e., 1,3-PD productivity and 1,3-PD yield, and their sensitivities with respect to uncertain time-delay are considered in the objective vector. The control variables in this problem are the feeding rate of glycerol, the switching instants and the terminal time of the process. By introducing an auxiliary dynamic system to calculate the objective sensitivities and performing a time-scaling transformation, we obtain an equivalent multi-objective optimal switching control problem in standard form. We then convert the equivalent multi-objective optimal control problem into a sequence of single-objective optimal switching control problems by using a modified normal boundary intersection method. A novel gradient-based single-objective solver combining control parameterization with constraint transcription technique is developed to solve these resulting singleobjective optimal control problems. Finally, numerical results are provided to verify the effectiveness of the proposed solution approach.

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“…Methods for estimating the values of these uncertain parameters using experimental data are given in [18,19,[29][30][31][32]. The following estimates are used in [6]: …”

Section: Assumption 22mentioning

confidence: 99%

Robust Optimal Control of a Microbial Batch Culture Process

Cheng

Wang

Loxton

et al. 2014

J Optim Theory Appl

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This paper considers the microbial batch culture process for producing 1,3-propanediol (1,3-PD) via glycerol fermentation. Our goal was to design an optimal control scheme for this process, with the aim of balancing two (perhaps competing) objectives: (i) the process should yield a sufficiently high concentration of 1,3-PD at the terminal time and (ii) the process should be robust with respect to changes in various uncertain system parameters. Accordingly, we pose an optimal control problem, in which both process yield and process sensitivity are considered in the objective function. The control variables in this problem are the terminal time of the batch culture process and the initial concentrations of biomass and glycerol in the batch reactor. By performing a time-scaling transformation and introducing an auxiliary dynamic system to calculate process sensitivity, we obtain an equivalent optimal control problem Communicated by Mimmo Iannelli. 123J Optim Theory Appl in standard form. We then develop a particle swarm optimization algorithm for solving this equivalent problem. Finally, we explore the trade-off between process efficiency and process robustness via numerical simulations.

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Optimal parameter selection for nonlinear multistage systems with time-delays

Cited by 25 publications

References 37 publications

Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

Robust multi-objective optimal switching control arising in 1,3-propanediol microbial fed-batch process

Robust Optimal Control of a Microbial Batch Culture Process

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