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Novel non-uniform adaptive grid refinement control parameterization approach for biochemical processes optimization

BIOCHEMICAL ENGINEERING JOURNAL 2016年 111卷 63-74页

作者： Liu, Ping Li, Guodong Liu, Xinggao Zhang, Zeyin Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Zhejiang Peoples R China

Dynamic optimization is a very important way to increase the productivity or profitability of biochemical processes. As an efficient approach for solving these biochemical dynamic optimization problems, control vector parameterization encounters the difficulty of selecting an optimal discretization level which balances the computational cost with the desired solution quality to obtain high accuracy solution. To tackle this issue, a new slope analysis is proposed to analyze the control variables and discretization time grid, results find that low slope time grid nodes have less effect on the improvement of performance index and can be regarded as unnecessary nodes, while high ones are important time points. Based on this, a novel non-uniform adaptive grid refinement control parameterization approach is therefore presented, where the slope analysis is applied to refine or to coarsen the time grid so as to obtain a suitable discretization level with a small number of control intervals. By application in three well-known biochemical optimization problems, results show that the proposed method is able to achieve similar or even better performance indexes with small numbers of control intervals and lower computational costs. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Bioprocess optimization Biochemical processes Grid refinement Non-uniform grid control parameterization Dynamic optimization

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Train Driving Strategy Optimization Using control parameterization Enhancing Technique 6

Train Driving Strategy Optimization Using Control Parameteri...

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6th IEEE International Conference on control System, Computing and Engineering (ICCSCE)

作者： Zhong, Weifeng Xu, Hongze Zhang, Wenjing Wang, Longsheng Beijing Jiaotong Univ Sch Elect & Informat Engn Beijing Peoples R China China Acad Railway Sci Signal & Commun Res Inst Beijing Peoples R China

ISBN: (纸本)9781509011780

Train energy consumption accounts for the largest proportion of total energy consumption in railway systems. Applying the optimal driving strategy is an important way to reduce train energy consumption. In this paper, an efficient numerical approach - control parameterization enhancing technique (CPET) is employed to determine the optimal train driving strategy, which is essentially a problem of optimal control. Using CPET, the train control forces are indicated by piecewise constant function with variable switching nodes. Then, CPET transforms the original problem of optimal train control into a nonlinear optimization problem by considering both the piecewise constant control values on each subinterval and the lengths of the subintervals as decision parameters. Finally, the transformed optimization problem is solved efficiently by using an exact penalty method to handle the train speed constraint and applying a sensitivity approach to obtain the gradient of the cost function. A case study is carried out to demonstrate that the optimal driving strategy obtained by the CPET is more energy-efficient than that obtained by the traditional control parameterization method under same conditions.

关键词： Train Driving Strategy Energy-efficient Train control control parameterization Optimal control

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Energy-efficient Train Reference Speed Profile Optimization Using control parameterization Method 35

Energy-efficient Train Reference Speed Profile Optimization ...

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第35届中国控制会议

作者： ZHONG Weifeng XU Hongze ZHANG Wenjing School of Electronic and Information Engineering Beijing Jiaotong University

ISBN: (纸本)9781509009107

With the expansion of high-speed railway network, the issue of train energy consumption becomes more serious and attracts much greater concerns. One of the important ways of saving energy is to find the energy-efficient train reference profile, which actually is a problem of optimal control. In this paper, the control parameterization method, a general and efficient numerical approach, is employed to solve the optimal train control problem. The objective function is to minimize the train energy consumption with a penalty on the control variation subjected to fixed travel time, traction and braking forces restriction and safety speed limit. Using the control parameterization technique, the train control force is approximated by a piecewise-constant function and the original train control problem is transformed into a nonlinear programming problem which can be solved efficiently. The numerical results indicate that the proposed method can obtain the optimal train reference profile which guarantees minimum energy consumption. Moreover, by increasing the penalty factor against control variation, the smoothness of train reference profile is significantly improved while the train energy consumption is almost unchanged.

关键词： Energy-efficient Train control Reference Speed Profile control parameterization control Variation

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parameterization optimal control of an unsteady partial differential equations with convection term by an improved three-term spectrum conjugate gradient algorithm

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MEASUREMENT & control 2024年第4期57卷 341-360页

作者： Yu, Yang Wang, Yu Pang, Xinfu Yang, Guodong Zhang, Fengqi Qi, Yiwen Shenyang Aerosp Univ Sch Automat Shenyang Peoples R China Shanghai Univ Sch Mechatron Engn & Automat Shanghai Peoples R China Shenyang Inst Engn Sch Automat Shenyang Peoples R China Shenyang Aerosp Univ 37 Daoyi South St Shenyang 110136 Liaoning Peoples R China

The unsteady partial differential equations (UPDE) with convection term gives a clear descriptions for the solidification process of a slab in dynamic production of continuous casting. To give a suitable setting value of secondary cooling water flow rate for the dynamic control system, this study investigates an optimal control problem (OCP) of UPDE with convection term. Firstly, control vector discretization of OCP and the solution of UPDE are given. Secondly, due to the rapidity for gradient, this paper analyzes the expression of the gradient calculation method based on Hamiltonian function costate system by approximate treatment, matrix calculation and composite trapezoidal integral method. Thirdly, an improved three-term spectrum conjugate gradient algorithm (ITSCGA) is proposed to solve the OCP of UPDE, and the global convergence of the ITSCGA is demonstrated. Lastly, the performance of ITSCGA is demonstrated by experimental simulations. The results demonstrate that the ITSCGA provides a smaller temperature fluctuations, and improves the quality of a slab.

关键词： control parameterization unsteady partial differential equations optimal control three-term spectrum conjugate gradient algorithm dynamic process

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On Combining Neighbouring Extremals with control parameterization 34

On Combining Neighbouring Extremals with Control Parameteriz...

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34th Chinese control Conference (CCC)

作者： Liu, Chongyang Lin, Qun Loxton, Ryan Teo, Kok Lay Shandong Inst Business & Technol Sch Math & Informat Sci Yantai 264005 Peoples R China Curtin Univ Dept Math & Stat Perth WA 6102 Australia Zhejiang Univ Inst Cyber Syst & Control Hangzhou 310027 Zhejiang Peoples R China

ISBN: (纸本)9789881563897

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.

关键词： Nonlinear system Optimal feedback control control parameterization Neighbouring extremals

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Dynamic Optimization of Tokamak Plasmas via control parameterization and the Time-scaling Transformation 34

Dynamic Optimization of Tokamak Plasmas via Control Paramete...

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34th Chinese control Conference (CCC)

作者： Ren, Zhigang Xu, Chao Lin, Qun Loxton, Ryan Zhejiang Univ State Key Lab Ind Control Technol Hangzhou Zhejiang Peoples R China Curtin Univ Dept Math & Stat Perth WA Australia

ISBN: (纸本)9789881563897

Fusion nuclear reactions, in which multiple atomic nuclei collide to form a single atomic nucleus, can only occur at extremely high temperatures, where all matter is in the plasma state. In the majority of today's experimental fusion reactors, the fusion plasma is confined to a torus shape using a magnetic confinement system called a tokamak. The performance of a tokamak depends crucially on the current spatial profile, which is related to the poloidal magnetic flux. Accordingly, in this paper, we investigate a finite-time optimal control problem in which the aim is to drive the current spatial profile to within close proximity of a desired target profile, subject to a parabolic PDE governing the evolution of the poloidal magnetic flux. To solve this optimal control problem, we first use the finite element method to approximate the PDE model by an ODE model. Then, we apply the control parameterization and time-scaling techniques to obtain an approximate finite-dimensional optimization problem, which can be solved using sequential quadratic programming methods. Simulation results using experimental data from the DIII-D tokamak in San Diego, California demonstrate the effectiveness of the proposed approach.

关键词： Nuclear Fusion Current Profile control Finite Element Method control parameterization Time-scaling Transformation Dynamic Optimization

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Guaranteed-Cost controls of Minimal Variation: A Numerical Algorithm Based on control parameterization 33

Guaranteed-Cost Controls of Minimal Variation: A Numerical A...

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33rd Chinese control Conference (CCC)

作者： Loxton, Ryan Lin Qun Teo, Kok Lay Curtin Univ Dept Math & Stat Perth WA 6845 Australia Zhejiang Univ Inst Cyber Syst & Control Hangzhou 310003 Zhejiang Peoples R China

ISBN: (纸本)9781479947249

The optimal control literature is dominated by standard problems in which the system cost functional is expressed in the well-known Bolza form. Such Bolza cost functionals consist of two terms: a Mayer term (which depends solely on the final state reached by the system) and a Lagrange integral term (which depends on the state and control values over the entire time horizon). One limitation with the standard Bolza cost functional is that it does not consider the cost of control changes. Such costs should certainly be considered when designing practical control strategies, as changing the control signal will invariably cause wear and tear on the system's acutators. Accordingly, in this paper, we propose a new optimal control formulation that balances system performance with control variation. The problem is to minimize the total variation of the control signal subject to a guaranteed-cost constraint that ensures an acceptable level of system performance (as measured by a standard Bolza cost functional). We first apply the control parameterization method to approximate this problem by a non-smooth dynamic optimization problem involving a finite number of decision variables. We then devise a novel transformation procedure for converting this non-smooth dynamic optimization problem into a smooth problem that can be solved using gradient-based optimization techniques. The paper concludes with numerical examples in fisheries and container crane control.

关键词： Optimal control Total variation control parameterization Nonlinear optimization

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HYBRID DYNAMIC OPTIMAL TRACKING control OF HYDRAULIC CYLINDER SPEED IN INJECTION MOLDING INDUSTRY PROCESS

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第7期19卷 5209-5229页

作者： Ren, Zhigang Wu, Guoshen Wu, Zongze Xie, Shengli Guangdong Univ Technol Sch Automat Guangdong HongKong Macao Joint Lab Smart Discrete Guangzhou 510006 Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Shenzhen Univ Coll Mechatron & Control Engn Shenzhen 518060 Peoples R China Guangdong Univ Technol Sch Automat Key Lab Intelligent Detect & Internet Things Mfg Minist Educ Guangzhou 510006 Peoples R China

Injection speed control is one of the most essential components in the injection molding process. It is critical to implement fast and reliable injection speed optimization control for the effective manufacturing of injection molding products. In this paper, the speed tracking control problem of the hydraulic cylinder of an injection molding machine driven by a typical servo motor is studied. An efficient two-stage optimization framework that leverages the ideas of both control parameterization (CP) and particle swarm optimization (PSO) is proposed for generating the optimal signal input to achieve the required injection speed tracking over a certain time. To this end, the dynamic model of the hydraulic system in the injection molding equipment is firstly established and the optimal controller design problem is transformed into sequential optimal parameter decision problems, and the explicit expressions of the gradient information of the objective function as well as the constraint on the parameters of the decision variables are derived. Then, the PSO combined with the CP and gradient-based algorithm is utilized to to solve the parameters of the controller efficiently. The two-stage optimization framework proposed in this paper can improve the convergence speed of the CP method and the precision of the PSO and easy-to-implement in engineering and industrial deployment. Finally, the feasibility and effectiveness of the proposed design method are verified by experimental simulations.

关键词： Industrial process injection molding optimal control control parameterization particle swarm optimization

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A Switching Time Optimization Strategy for Optimal control Problems

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JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF CHINA 2023年 1-22页

作者： Chen, Yin Yu, Chang-Jun Zhu, Xi Shanghai Univ Dept Math Shanghai 200444 Peoples R China

The time-scaling transformation is a widely used approach within the computational framework of control parameterization for optimizing the switching times of control variables. However, the conventional time-scaling transformation has the limitation that the switching times and the number of switches for each control component must be the same. In this paper, we present a novel technique to solve constrained optimal control problems that allows for adaptively optimizing the switching times for each control component. Numerical results demonstrate that this proposed method provides better flexibility in control strategy and yields improved performance.

关键词： Optimal control control parameterization Time-scaling transformation Sequential adaptive switching time optimization technique Co-state method

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Learning-PDE-Based Approximate Optimal control for an MHD System With Uncertainty Quantification

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第11期52卷 7185-7192页

作者： Chen, Tehuan Ren, Zhigang Lin, Guang Xu, Chao Ningbo Univ Sch Mech Engn & Mech Ningbo 315211 Zhejiang Peoples R China Shanghai Jiao Tong Univ Ningbo Artificial Intelligence Inst Ningbo 315000 Zhejiang Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Guangdong Peoples R China Chongqing Univ Posts & Telecommun Minist Educ Key Lab Ind Internet Things & Networked Control Chongqing 400065 Peoples R China Purdue Univ Dept Math W Lafayette IN 47907 USA Purdue Univ Sch Mech Engn W Lafayette IN 47907 USA Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China Zhejiang Univ Inst Cyber Syst & Control Hangzhou 310027 Zhejiang Peoples R China

Handling uncertainty is one of the most important challenges in real physical systems. In this article, we study an approximate optimal magnetic control strategy for a one-dimensional (1-D) magnetohydrodynamic (MHD) system with uncertainty quantification within the learning framework of the underlying MHD model. First, the MHD flow system is modeled by coupled partial differential equations (PDEs) wherein the Reynolds number is not deterministic but random. Then, the optimal magnetic control problem is formulated and reduced to a parameter selection problem with stochastic PDE constraints by means of the control parameterization method. Significantly different from the conventional sensitivity analysis and adjoint methods, a polynomial chaos expansion (PCE) based on a multifidelity model is developed to construct the underlying PDEs model by polynomial functions. Thus, the relationship between the objective function and the control sequence is derived explicitly, which, in turn, transforms the optimal parameter selection problem with stochastic PDE constraints into a typical algebraic optimization problem that can be easily solved by the existing nonlinear programming algorithm. Numerical simulations are illustrated to demonstrate the high performance of our proposed method.

关键词： Magnetohydrodynamics Mathematical models Optimal control Magnetic separation Uncertainty Linear programming Numerical models control parameterization multifidelity probabilistic collocation method optimal control uncertainty quantification

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