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Asynchronous switching and sparse discretization with time scaling for control vector parameterization optimal control

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ENGINEERING OPTIMIZATION 2025年第5期57卷 1263-1290页

作者： Wang, Hainan Gatzke, Edward P. Univ South Carolina Coll Engn & Comp Dept Chem Engn Columbia SC 29208 USA

This work introduces a novel approach for solving open-loop Optimal control Problems (OCPs) using multiple time grids, sparse discretization and a time scaling transformation. control vector parameterization (CVP) method parameterizes control variables to create a finite-dimensional problem. The Variable Time Nodes control vector parameterization (VTNCVP) discretization strategy allows each control component an independent time grid, offering enhanced input design flexibility and potentially yielding improved outcomes. A novel time scaling technique for OCPs with multiple time grids is presented that is easier to comprehend than existing methods and can circumvent some numerical difficulties. Additionally, Multiple Grid (MG)-Sparse Variable Time Nodes (MG-SVTN) is presented. This novel discretization strategy employs asynchronous switching with user-specified numbers of subdivisions for input controls, potentially yielding comparable objective function values to VTNCVP while reducing the dimensionality of decision variables. Two example problems with path constraints are solved using the methods.

关键词： Nonlinear optimal control control vector parameterization asynchronous time grid time scaling transformation sparse discretization method

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control vector parameterization-Based Adaptive Invasive Weed Optimization for Dynamic Processes

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CHEMICAL ENGINEERING & TECHNOLOGY 2018年第5期41卷 964-974页

作者： Tian, Jing Zhang, Panpan Wang, Yalin Liu, Xinggao Yang, Chunhua Lu, Jiangang Gui, Weihua Sun, Youxian Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol 38 Zheda Rd Hangzhou 310027 Zhejiang Peoples R China Cent South Univ Sch Informat Sci & Engn Lushan Rd Changsha 410083 Hunan Peoples R China

A novel optimal approach named invasive weed optimization-control vector parameterization (IWO-CVP) for chemical dynamic optimization problems is proposed where CVP is used to transform the problem into a nonlinear programming (NLP) problem and an IWO algorithm is then applied to tackle the NLP problem. To improve efficiency, a new adaptive dispersion IWO-based approach (ADIWO-CVP) is further suggested to maintain the exploration ability of the algorithm throughout the entire searching procedure. Several classic chemical dynamic optimization problems are tested and detailed comparisons are carried out among ADIWO-CVP, IWO-CVP, and other methods. The research results demonstrate that ADIWO-CVP not only is efficient, but also outperforms IWO-CVP in terms of both accuracy and convergence speed.

关键词： Adaptive dispersion control vector parameterization Dynamic optimization Invasive weed optimization Nonlinear programming

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A new sensitivity-based adaptive control vector parameterization approach for dynamic optimization of bioprocesses

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BIOPROCESS AND BIOSYSTEMS ENGINEERING 2017年第2期40卷 181-189页

作者： Wang, Liwei Liu, Xinggao Zhang, Zeyin Zhejiang Univ Coll Control Sci & Engn Hangzhou 310027 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

Dynamic optimization is a very effective way to increase the profitability or productivity of bioprocesses. As an important method of dynamic optimization, the control vector parameterization (CVP) approach needs to select an optimal discretization level to balance the computational cost with the desired solution quality. A new sensitivity-based adaptive refinement method is therefore proposed, by which new time grid points are only inserted where necessary and unnecessary points are eliminated so as to obtain economic and effective discretization grids. Moreover, considering that traditional refinement methods may cost a lot to get the high-quality solutions of some bioprocess problems, whose performance indices are sensitive to some significant time points, an optimization technique is further proposed and embedded into the new sensitivity-based CVP approach to efficiently solve these problems. The proposed methods are applied to two wellknown bioprocess optimization problems and the results illustrate their effectiveness.

关键词： Dynamic optimization Bioprocesses control vector parameterization Adaptive grid refinement Sensitivity

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An improved slope-based adaptive control vector parameterization method for dynamic programming

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ALEXANDRIA ENGINEERING JOURNAL 2024年 86卷 49-55页

作者： Li, Tai-Fang Dang, Lanqing Cai, Lihou Bohai Univ Coll Control Sci & Engn Jinzhou 121013 Peoples R China

control vector parameterization method is the most commonly used numerical computation method in solving dynamic programming problems. However, to balance the expected trajectory and the computational cost, this method faces difficulties in dividing the optimal discretization time grid. In this paper, we propose an effective control approach for non-uniform adaptive grid division. By analyzing the slope change trend of the control parameter, time nodes are adaptively refined by merging time grids with gentle slopes to remove unnecessary time nodes and adding time nodes to time grids with steep slopes to improve function approximation accuracy. Eventually, we obtain an adaptive time grid division method under which the trajectory of discretization control parameter is more approximate to the optimal control trajectory. Under the condition of intuitive slope information, the proposed method can achieve better performance with fewer optimization parameters and shorter computation time. Finally, the proposed method is applied to solve a classic optimal control problem and the obtained results are compared with the traditional control vector parameterization method. By comparison through the example, our proposed method can overcome the contradiction between approximation accuracy and computational cost in control vector parameterization method and improve the optimization efficiency.

关键词： Dynamic programming control vector parameterization Adaptive grid division Slope analysis

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A slope-based automatic identification and optimization of key time nodes method for adaptive control vector parameterization

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND control 2024年

作者： Dang, Lanqing Ye, Shijin Li, Tai-Fang Bohai Univ Coll Control Sci & Engn Jinzhou 121013 Peoples R China

control vector parameterization is a mainstream numerical approach for solving dynamic programming problems. By discretizing the entire time domain into a grid of time nodes, an infinite-dimensional optimal control problem can be transformed into a finite-dimensional static optimization problem. Despite the attractive advantages of high solution accuracy and ease of implementation of control vector parameterization, the rationality of time grid partitioning significantly influences the efficiency of the solution and the approximating accuracy of the optimal control trajectory. In the traditional control vector parameterization method, the time grid is typically set beforehand and remains static in the optimization process, which has a direct impact on how closely the solution result approximates the optimal control trajectory. To address the conflict of accurate approximations and computational time, we propose a slope-based automatic identification and optimization of key time nodes method for adaptive control vector parameterization, which not only optimizes merging and inserting time nodes but also incorporates automatic identification of key time nodes. Through a simulation example, we verify that this improved method can reduce computation time, enhance approximation accuracy, and achieve higher optimization efficiency.

关键词： control vector parameterization slope-based analysis identification and optimization key time nodes adaptive grid division

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A Fourier-based control vector parameterization for the optimization of nonlinear dynamic processes with a finite terminal time

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COMPUTERS & CHEMICAL ENGINEERING 2020年第0期134卷 106721-000页

作者： Nadia Pantano, M. Cecilia Fernandez, M. Ortiz, Oscar A. Scaglia, Gustavo J. E. Vega, Jorge R. Univ Nacl San Juan Inst Ingn Quim CONICET Av Libertador San Martin OJ5400ARL RA-1109 San Juan Argentina CONICET UNL Inst Desarrollo Tecnol Ind Quim INTEC Guemes 3450S3000GLN Santa Fe Argentina UTN FRSF CIESE Ctr Invest & Desarrollo Ingn Elect & Sistemas Ene Lavaisse 610S3004EWB Santa Fe Argentina

In this paper, a novel strategy for finding the optimal operation profiles for nonlinear dynamic processes is developed. Based on the direct sequential stochastic framework for dynamic optimization, this work proposes a technique based on Fourier series for the control vector parameterization, as an alternative to the traditional methods. This approach has the advantage of choosing a high degree of smoothness to avoid sharp changes for the input variables, which is preferred in most chemical and biological processes. On the other hand, when several arcs are present in the qualitative optimal profile, the number of parameters can be increased for a better approximation. The proposed strategy was applied to four well-studied nonlinear processes, covering batch and fed-batch reactors, and multi-input systems. The algorithm was tested through simulations. Good performances were obtained in comparison to some previous results available in the literature. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Fourier approach control vector parameterization Nonlinear systems Dynamic optimization

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Dynamic optimization of chemical engineering problems using a control vector parameterization method with an iterative genetic algorithm

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ENGINEERING OPTIMIZATION 2013年第9期45卷 1129-1146页

作者： Qian, Feng Sun, Fan Zhong, Weimin Luo, Na E China Univ Sci & Technol Key Lab Adv Control & Optimizat Chem Proc Minist Educ Shanghai 200237 Peoples R China

An approach that combines genetic algorithm (GA) and control vector parameterization (CVP) is proposed to solve the dynamic optimization problems of chemical processes using numerical methods. In the new CVP method, control variables are approximated with polynomials based on state variables and time in the entire time interval. The iterative method, which reduces redundant expense and improves computing efficiency, is used with GA to reduce the width of the search region. Constrained dynamic optimization problems are even more difficult. A new method that embeds the information of infeasible chromosomes into the evaluation function is introduced in this study to solve dynamic optimization problems with or without constraint. The results demonstrated the feasibility and robustness of the proposed methods. The proposed algorithm can be regarded as a useful optimization tool, especially when gradient information is not available.

关键词： control vector parameterization iterative genetic algorithm dynamic optimization chemical engineering

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An improved smoothing technique-based control vector parameterization method for optimal control problems with inequality path constraints

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OPTIMAL control APPLICATIONS & METHODS 2017年第4期38卷 586-600页

作者： Liu, Ping Li, Xiangyu Liu, Xinggao Hu, Yunqing Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China CSR Zhuzhou Inst Co Ltd Zhuzhou 412001 Hunan Peoples R China

An improved control vector parameterization (CVP) method is proposed to solve optimal control problems with inequality path constraints by introducing the l(1) exact penalty function and a novel smoothing technique. Both the state and control variables are allowed to appear explicitly in the inequality path constraints simultaneously. By applying the penalty function and smoothing technique, all the inequality path constraints are firstly reformulated as non-differentiable penalty terms and incorporated into the objective function. Then, the penalty terms are smoothed by using a novel smooth function, leading to a smooth optimal control problem with no inequality path constraints. With discretizing the control space, a corresponding nonlinear programming (NLP) problem is derived, and error between the NLP problem and the original problem is discussed. Results reveal that if the smoothing parameter is sufficiently small, the solution of the NLP problem is approximately equal to the original problem, which shows the convergence of the proposed method. After clarifying some theories of the proposed approach, a concomitant numerical algorithm is put forward with furnishing the updating rules of both the penalty parameter and smoothing parameter. Simulation examples verify the advantages of the proposed method for tackling nonlinear optimal control problems with different inequality path constraints. Copyright (c) 2016 John Wiley & Sons, Ltd.

关键词： nonlinear optimal control inequality path constraints control vector parameterization penalty function smoothing technique

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A novel non-uniform control vector parameterization approach with time grid refinement for flight level tracking optimal control problems

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ISA TRANSACTIONS 2018年 73卷 66-78页

作者： Liu, Ping Li, Guodong Liu, Xinggao Xiao, Long Wang, Yalin Yang, Chunhua Gui, Weihua Chongqing Univ Posts & Telecommun Coll Automat Key Lab Ind Wireless Network & Networked Control Chongqing 400065 Peoples R China Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China China Acad Elect & Informat Technol Beijing 100041 Peoples R China Cent S Univ Sch Informat Sci & Engn Changsha 410083 Hunan Peoples R China

High quality control method is essential for the implementation of aircraft autopilot system. An optimal control problem model considering the safe aerodynamic envelop is therefore established to improve the control quality of aircraft flight level tracking. A novel non-uniform control vector parameterization (CVP) method with time grid refinement is then proposed for solving the optimal control problem. By introducing the Hilbert-Huang transform (HHT) analysis, an efficient time grid refinement approach is presented and an adaptive time grid is automatically obtained. With this refinement, the proposed method needs fewer optimization parameters to achieve better control quality when compared with uniform refinement CVP method, whereas the computational cost is lower. Two well-known flight level altitude tracking problems and one minimum time cost problem are tested as illustrations and the uniform refinement control vector parameterization method is adopted as the comparative base. Numerical results show that the proposed method achieves better performances in terms of optimization accuracy and computation cost;meanwhile, the control quality is efficiently improved. (C) 2017 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Flight level tracking Optimal control control vector parameterization Hilbert-Huang transform Time grid refinement

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An iterative multi-objective particle swarm optimization-based control vector parameterization for state constrained chemical and biochemical engineering problems

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BIOCHEMICAL ENGINEERING JOURNAL 2015年 103卷 138-151页

作者： Zhang, Panpan Chen, Hongmei Liu, Xinggao Zhang, Zeyin Zhejiang Univ Dept Control Sci & Engn Inst Ind Proc Control State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China Weifang Univ Inst Electromech & Vehicle Engn Weifang 262061 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Zhejiang Peoples R China

Dynamic optimization of the state constrained chemical and biochemical engineering problems has always been the research hotspot due to the difficulties of handling constraints. In this paper, a novel approach, CVP-IMOPSO, is presented to tackle this kind of problems, where the original optimization problem is firstly converted into a multi-objective dynamic optimization problem based on a method of handling state constraint;and control vector parameterization (CVP) is then applied to transform the resulting infinite dimensional problem into a nonlinear programming (NLP) problem;finally, an efficient iterative multi-objective particle swarm optimization (IMOPSO), embedded with an region reduction strategy, is proposed to tackle this MOO problem. This strategy reduces the search space gradually during the iteration process so as to further promote the convergence rate and diversity of MOPSO. Three well-known classic optimization problems for chemical and biochemical engineering processes have been tested as illustration, and the detailed comparisons among IMOPSO, MOPSO and NSGA-II are carried out for seven benchmark problems. The research results not only show that the proposed IMOPSO is an efficient algorithm for MOO problems, but also reveal the effectiveness of the proposed approach. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Dynamic optimization Multi-objective particle swarm optimization control vector parameterization Multi-objective optimization Region reduction strategy State constrained engineering problems

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