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SelectedWorks

Chongyang Liu

Articles 1 - 23 of 23

Full-Text Articles in Physical Sciences and Mathematics

Optimal Control Of A Switched Autonomous System With Time Delay Arising In Fed-Batch Processes, Chongyang Liu Apr 2015

Optimal Control Of A Switched Autonomous System With Time Delay Arising In Fed-Batch Processes, Chongyang Liu

Chongyang Liu

In this paper, we propose a switched autonomous system with time delay to model the 1,3-propanediol (1,3-PD) production in a fed-batch process. Taking the switching instants and the terminal time as the control variables, we formulate a constrained time-delayed optimal control (CTOC) problem to optimize the 1,3-PD production process. Using a time-scaling transformation and parametrizing the switching instants into new parameters, an equivalent CTOC problem is investigated. A numerical solution method is then developed to seek the optimal control strategy. This method is based on the constraint transcription technique and the gradients of the cost functional together with those of …

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On Combining Neighbouring Extremals With Control Parameterization, Chongyang Liu, Qun Lin, Ryan Loxton, Kok Lay Teo Jan 2015

On Combining Neighbouring Extremals With Control Parameterization, Chongyang Liu, Qun Lin, Ryan Loxton, Kok Lay Teo

Chongyang Liu

In this paper, we consider the neighbouring extremals for a class of optimal control problems with control constraints. We first solve the optimal control problem using control parameterization method to obtain the optimal open-loop control and the optimal reference state. Then, a neighbouring feedback control law is derived for small state perturbations caused by changes on reference state at switching times.

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Nonlinear State-Dependent Impulsive System In Fed-Batch Culture And Its Optimal Control, Bangyu Shen, Xiaojing Wang, Chongyang Liu Jan 2015

Nonlinear State-Dependent Impulsive System In Fed-Batch Culture And Its Optimal Control, Bangyu Shen, Xiaojing Wang, Chongyang Liu

Chongyang Liu

In this paper, a nonlinear impulsive controlled system, in which the volume of feeding is taken as the control function, is proposed to formulate the fed-batch fermentation process.In the system, both impulsive moments and jumps size of state are state-dependent. Some important properties of the system are investigated. To maximize the concentration of target product at the terminal time, an optimal control model involving the nonlinear state-dependent impulsive controlled system is presented.The optimal control problem is subject to the continuous state inequality constraint and the control constraint. The existence of optimal control is also obtained. In order to derive the …

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Horizontal Well’S Path Planning: An Optimal Switching Control, Zhaohua Gong, Kok Lay Teo, Chongyang Liu, Enmin Feng Jan 2015

Horizontal Well’S Path Planning: An Optimal Switching Control, Zhaohua Gong, Kok Lay Teo, Chongyang Liu, Enmin Feng

Chongyang Liu

In this paper, we consider a three-dimensional horizontal well’s path planning problem, where the well’s path evolves as a combination of several constant-curvature smooth turn segments. The problem is formulated as an optimal switching control problem subject to continuous state inequality constraints. By applying the time-scaling transformation and constraint transcription in conjunction with local smooth approximation technique, the optimal switching control problem is approximated by a sequence of optimal parameter selection problems with only box constraints, each of which is solvable by gradient-based optimization techniques. The optimal path planning problems of the wells Ci-16-Cp146 and Jin27 in Liaohe oil field …

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Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, Chongyang Liu, Zhaohua Gong Jan 2014

Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, Chongyang Liu, Zhaohua Gong

Chongyang Liu

The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently optimal control …

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Sensitivity Analysis And Parameter Identification For A Nonlinear Time-Delay System In Microbial Fed-Batch Process, Chongyang Liu Jan 2014

Sensitivity Analysis And Parameter Identification For A Nonlinear Time-Delay System In Microbial Fed-Batch Process, Chongyang Liu

Chongyang Liu

Developing suitable dynamic models of bioprocess is a difficult issue in bioscience. In this paper, considering the microbial metabolism mechanism, i.e., the production of new biomass is delayed by the amount of time it takes to metabolize the nutrients, in glycerol bioconversion to 1,3-propanediol, we propose a nonlinear time-delay system to formulate the fed-batch fermentation process. Some important properties are also discussed. Then, in view of the effect of time-delay and the high number of kinetic parameters in the system, the parametric sensitivity analysis is used to determine the key parameters. Finally, a parameter identification model is presented and a …

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Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo Jan 2014

Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo

Chongyang Liu

In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the …

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A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, Chongyang Liu, Ryan Loxton, Kok Lay Teo Jan 2014

A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, Chongyang Liu, Ryan Loxton, Kok Lay Teo

Chongyang Liu

This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time-delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system …

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Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo Jan 2014

Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo

Chongyang Liu

In this paper, we consider a novel dynamic optimization problem for nonlinear multistage systems with time-delays. Such systems evolve over multiple stages, with the dynamics in each stage depending on both the current state of the system and the state at delayed times. The optimization problem involves choosing the values of the time-delays, as well as the values of additional parameters that influence the system dynamics, to minimize a given cost functional. We first show that the partial derivatives of the system state with respect to the time-delays and system parameters can be computed by solving a set of auxiliary …

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Optimal Control For A Nonlinear Time-Delay System In Fed-Batch Fermentation, Chongyang Liu, Zhaohua Gong, Enmin Feng Oct 2013

Optimal Control For A Nonlinear Time-Delay System In Fed-Batch Fermentation, Chongyang Liu, Zhaohua Gong, Enmin Feng

Chongyang Liu

The main control goal in fed-batch fermentation is to maximize yield of target product and reduce operation costs. In this paper, we propose a controlled nonlinear time-delay system, in which the flow rate of glycerol is taken as the control function and the terminal time of the fermentation as the optimization variable, to model the 1,3-propanediol (1,3-PD) production in fed-batch process. Taking the mass of 1,3-PD per unit time as the performance index, we formulate a constrained optimal control model with free terminal time to optimize the production process. Using a time-scale transformation, the optimal control problem is equivalently transcribed …

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Optimal Switching Control Of A Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin Jan 2012

Optimal Switching Control Of A Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin

Chongyang Liu

Considering the hybrid nature in fed-batch culture of glycerol biconversion to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae, we propose a state-based switching dynamical system to describe the fermentation process. To maximize the concentration of 1,3-PD at the terminal time, an optimal switching control model subject to our proposed switching system and constraints of continuous state inequality and control function is presented. Because the number of the switchings is not known a priori, we reformulate the above optimal control problem as a two-level optimization problem. An optimization algorithm is developed to seek the optimal solution on the basis of a heuristic approach …

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Nonlinear Dynamical Systems Of Fed-Batch Fermentation And Their Optimal Control, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin Jan 2012

Nonlinear Dynamical Systems Of Fed-Batch Fermentation And Their Optimal Control, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin

Chongyang Liu

In this article, we propose a controlled nonlinear dynamical system with variable switching instants, in which the feeding rate of glycerol is regarded as the control function and the moments between the batch and feeding processes as switching instants, to formulate the fed-batch fermentation of glycerol bioconversion to 1,3-propanediol (1,3-PD). Some important properties of the proposed system and its solution are then discussed. Taking the concentration of 1,3-PD at the terminal time as the cost functional, we establish an optimal control model involving the controlled nonlinear dynamical system and subject to continuous state inequality constraints. The existence of the optimal …

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Modeling And Parameter Identification Involving 3-Hydroxypropionaldehyde Inhibitory Effects In Glycerol Continuous Fermentation, Zhaohua Gong, Chongyang Liu, Yongsheng Yu Jan 2012

Modeling And Parameter Identification Involving 3-Hydroxypropionaldehyde Inhibitory Effects In Glycerol Continuous Fermentation, Zhaohua Gong, Chongyang Liu, Yongsheng Yu

Chongyang Liu

Mathematical modeling and parameter estimation are critical steps in the optimization of biotechnological processes. In the 1,3-propanediol (1,3-PD )production by glycerol fermentation process under anaerobic conditions, 3-hydroxypropionaldehyde (3-HPA) accumulation would arouse an irreversible cessation of the fermentation process. Considering 3-HPA inhibitions to cells growth and to activities of enzymes, we propose a novel mathematical model to describe glycerol continuous cultures. Some properties of the above model are discussed. On the basis of the concentrations of extracellular substances, a parameter identification model is established to determine the kinetic parameters in the presented system. Through the penalty function technique combined with an …

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Optimal Control Of A Fed-Batch Fermentation Involving Multiple Feeds, Chongyang Liu, Zhaohua Gong, Zhaoyi Huo, Bangyu Shen Jan 2012

Optimal Control Of A Fed-Batch Fermentation Involving Multiple Feeds, Chongyang Liu, Zhaohua Gong, Zhaoyi Huo, Bangyu Shen

Chongyang Liu

A nonlinear dynamical system, in which the feed rates of glycerol and alkali are taken as the control functions, is first proposed to formulate the fed-batch culture of 1,3-propanediol (1,3-PD) production. To maximize the 1,3-PD concentration at the terminal time, a constrained optimal control model is then presented. A solution approach is developed to seek the optimal feed rates based on control vector parametrization method and improved differential evolution algorithm. The proposed methodology yielded an increase by 32.17% of 1,3-PD concentration at the terminal time.

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Optimal Control Of Switched Autonomous Systems In Microbial Fed-Batch Cultures, Chongyang Liu, Enmin Feng Jan 2011

Optimal Control Of Switched Autonomous Systems In Microbial Fed-Batch Cultures, Chongyang Liu, Enmin Feng

Chongyang Liu

A switched autonomous system is proposed to formulate the fed-batch culture process by taking the switching instants between the feed and batch processes as control variables. To maximize the concentration of 1,3-propanediol (1,3-PD) at the terminal time, an optimal control model subject to our proposed switched autonomous system and continuous state inequality constraints is then presented.Acomputational approach is developed to find the optimal switching instants in two aspects. On the one hand, the constraint transcription and smoothing techniques are applied to dealing with the continuous state inequality constraints; on the other hand, the first and the second derivatives of the …

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Optimal Control Of A Switched System In Microbial Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng Jul 2010

Optimal Control Of A Switched System In Microbial Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng

Chongyang Liu

The main control goal in fed-batch fermentation process is to get a high concentration of production. In this paper, by taking the feed rate of glycerol as the control function, a nonlinear switched system is proposed to formulate the fed-batch fermentation process of glycerol to 1,3-propanediol (1,3-PD). To maximize the concentration of 1,3-PD at the terminal time, an optimal switching control model subject to constraints of continuous state inequality and control function is presented. A computational approach is developed to seek the optimal solution in two aspects. On the one hand, the control parametrization enhancing transform together with the control …

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Modeling And Optimal Control Of A Nonlinear Dynamical System In Microbial Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng Jan 2010

Modeling And Optimal Control Of A Nonlinear Dynamical System In Microbial Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng

Chongyang Liu

The mathematical model and optimal control of microbial fed-batch fermentation is considered in this paper. Since it is decisive for increasing the productivity of 1,3-propanediol (1,3-PD) to optimize the feeding rate of glycerol and the switching instants between the batch and feeding processes in the fermentation process, we propose a new nonlinear dynamical system to formulate the process. In the system, the switching instants are variable and the feeding rate of glycerol is regarded as the control function. Some important properties of the proposed system and its solution are then discussed. To maximize the concentration of 1,3-PD at the terminal …

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Computational Method For Inferring Objective Function Of Glycerol Metabolism In Klebsiella Pneumoniae, Zhaohua Gong, Chongyang Liu, Enmin Feng, Qingrui Zhang Jan 2009

Computational Method For Inferring Objective Function Of Glycerol Metabolism In Klebsiella Pneumoniae, Zhaohua Gong, Chongyang Liu, Enmin Feng, Qingrui Zhang

Chongyang Liu

Flux balance analysis (FBA) is an effective tool in the analysis of metabolic network. It can predict the flux distribution of engineered cells, whereas the accurate prediction depends on the reasonable objective function. In this work, we propose two nonlinear bilevel programming models on anaerobic glycerol metabolism in Klebsiella pneumoniae (K. pneumoniae) for 1,3-propanediol (1,3-PD) production. One intends to infer the metabolic objective function, and the other is to analyze the robustness of the objective function. In view of the models’ characteristic an improved genetic algorithm is constructed to solve them, where some techniques are adopted to guarantee all chromosomes …

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Modelling And Optimal Control For Nonlinear Multistage Dynamical System Of Microbial Fed-Batch Culture, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin Jan 2009

Modelling And Optimal Control For Nonlinear Multistage Dynamical System Of Microbial Fed-Batch Culture, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin

Chongyang Liu

In this paper, we propose a new controlled multistage system to formulate the fed-batch culture process of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD) by regarding the feeding rate of glycerol as a control function. Compared with the previous systems, this system doesn’t take the feeding process as an impulsive form, but a time-continuous process, which is much closer to the actual culture process. Some properties of the above dynamical system are then proved. To maximize the concentration of 1,3-PD at the terminal time, we develop an optimal control model subject to our proposed controlled multistage system and continuous state inequality constraints. …

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Optimal Control And Properties Of Nonlinear Multistage Dynamical System For Planning Horizontal Well Paths, Zhaohua Gong, Chongyang Liu, Enmin Feng Jan 2009

Optimal Control And Properties Of Nonlinear Multistage Dynamical System For Planning Horizontal Well Paths, Zhaohua Gong, Chongyang Liu, Enmin Feng

Chongyang Liu

The goal of planning a horizontal well path is to obtain a trajectory that arrives at a given target subject to various constraints. In this paper, the optimal control problem subject to a nonlinear multistage dynamical system (NMDS) for horizontal well paths is investigated. Some properties of the multistage system are proved. In order to derive the optimality conditions, we transform the optimal control problem into one with control constraints and inequality-constrained trajectories by defining some functions. The properties of these functions are then discussed and optimality conditions for optimal control problem are also given. Finally, an improved simplex method …

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Optimal Control For Nonlinear Dynamical System Of Microbial Fed-Batch Culture, Chongyang Liu Jan 2009

Optimal Control For Nonlinear Dynamical System Of Microbial Fed-Batch Culture, Chongyang Liu

Chongyang Liu

In fed-batch culture of glycerol bio-dissimilation to 1, 3-propanediol (1, 3-PD), the aim of adding glycerol is to obtain as much 1, 3-PD as possible. So a proper feeding rate is required during the process. Taking the concentration of 1, 3-PD at the terminal time as the performance index and the feeding rate of glycerol as the control function, we propose an optimal control model subject to a nonlinear dynamical system and constraints of continuous state and non-stationary control. A computational approach is constructed to seek the solution of the above model in two aspects. On the one hand we …

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Optimal Switching Control For Microbial Fed-Batch Culture, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin Jan 2008

Optimal Switching Control For Microbial Fed-Batch Culture, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin

Chongyang Liu

In fed-batch culture of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD), the aim of adding glycerol is to obtain as much 1,3-PD as possible. Hence, a proper feed strategy is required during the process. In this paper, we present an optimal switching control model based on our proposed controlled switching system. Some properties of the controlled switching system are obtained. Subsequently, we prove the existence of optimal control. In order to deduce the optimality conditions, we transcribe the optimal switching control model into an equivalent one with fixed switching instants and parameters. Finally, the optimality conditions of the equivalent problem are investigated …

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Identification Of Intracellular Kinetic Parameters In Continuous Bioconversion Of Glycerol By Klebsiella Pneumoniae, Enmin Feng, Chongyang Liu, Zhaohua Gong, Yaqin Sun Jan 2008

Identification Of Intracellular Kinetic Parameters In Continuous Bioconversion Of Glycerol By Klebsiella Pneumoniae, Enmin Feng, Chongyang Liu, Zhaohua Gong, Yaqin Sun

Chongyang Liu

In this paper, we propose a hybrid nonlinear dynamical system to describe the concentration changes of extracellular and intracellular substances of glycerol bioconversion to 1,3- propanedol (1,3-PD) in microbial continuous cultures. It is proved that the solution to the system exists and is continuous with respect to kinetic parameters. Subsequently, a novel quantitative definition of biological robustness is investigated. We present a performance index based on experiment data of extracellular concentrations and biological robustness. Taking the proposed hybrid nonlinear dynamical system as a constraint, we establish an identification model to determine the most reasonable metabolic pathway and optimal kinetic parameters. …

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