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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, Chongyang Liu, Zhaohua Gong
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 …
Sensitivity Analysis And Parameter Identification For A Nonlinear Time-Delay System In Microbial Fed-Batch Process, Chongyang Liu
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 …
Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo
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 …
A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, Chongyang Liu, Ryan Loxton, Kok Lay Teo
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 …
Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo
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 …