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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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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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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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Transition trajectory generation with time-scaled trigonometric series control parameterization

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Aerospace Systems 2022年第4期5卷 523-530页

作者： Hong, Haichao Piprek, Patrick Hu, Shiqiang Holzapfel, Florian Institute of Flight System Dynamics Technical University of Munich Garching 85748 Germany School of Aeronautics and Astronautics Shanghai Jiao Tong University Shanghai 200240 China

This paper is concerned with shaping the time behavior of controls for generating transition trajectories. Parameterizing controls with trigonometric series enables infinite differentiability with respect to time, which is very appealing in real operations. In practice, one may desire the controls to have a specific distribution over time. However, to achieve this usually relies on judicious selection of the cost function. To this end, this paper introduces a time-scaling transformation for the trigonometric series. It yields an intuitive and flexible way to design the controls tailored to the desired shape of a transition maneuver. The process does not rely on additional design effort for the cost function. The proposed method is applied to generating a transition trajectory that converges to the desired condition earlier in comparison to the unscaled formulation. Numerical results demonstrate the effectiveness of the proposed method. © 2022, The Author(s).

关键词： control parameterization Time scaling Trajectory generation Trigonometric series

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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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Dynamic optimal control of flow front position in injection molding process: A control parameterization-based method

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JOURNAL OF PROCESS control 2023年 132卷

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

High dynamic and precise control of process variables within permissible limits is the key to high product quality in the injection molding industry. Among these variables, the injection flow rate of molten polymer is particularly significant. In this paper, an effective optimal open-loop and state feedback controller design method is designed to realize the optimal tracking control of the melt polymer flow front position flow of melt polymer fluid during injection molding. To this end, the dynamic model of the filling process is firstly established, taking into account the nonlinearity of hydraulic control system and the effect of molten polymer flow on the dynamics of the injection ram, and then the dynamic optimal tracking control problem of flow front position of molten polymer in injection molding machine is proposed. Then, an open-loop controller and a multi-level feedback control law are well designed, wherein the control signal and the control feedback kernels are parameterized by control parameterization. The controller design problems are transformed into sequential optimal parameter decision problems. The explicit expressions of the gradient information of the objective function and constraints on the parameters of the decision variables are solved by using the state sensitivity equation analysis method, and the gradient information is combined with the nonlinear programming algorithm to solve the optimization problems efficiently. Finally, the viability and effectiveness of the proposed design method are verified by numerical simulations.

关键词： Injection molding Optimal control control parameterization Dynamic optimization State feedback

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OPTIMAL control OF MULTIPLE-TIME DELAYED SYSTEMS BASED ON THE control parameterization METHOD

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The ANZIAM Journal 2012年第1期53卷 68-86页

作者： W. H. GUI X. Y. SHEN N. CHEN C. H. YANG L. Y. WANG School of Information Science and Engineering Central South University Changsha 410083 PR China (email: gwh@*** shxy-0501@*** ningchen@*** ychh@***) School of Electrical Engineering and Renewable Energy China Three Gorges University Yichang 443002 PR China (email: wly@***)

In this paper we study optimal control computation based on the control parameterization method for a class of optimal control problems involving nonlinear systems with multiple time delays subject to continuous state inequality constraints. Both the state and the control are allowed to have different time delays, and they are uncorrelated in this system. The control of the dynamical system is approximated by a piecewise constant function whose heights are taken as decision vectors. The formulae for computing the gradients of the cost and constraint functions are then derived. Based on this, a computational method for finding the optimal control is developed by utilizing the Sequential Quadratic Programming (SQP) algorithm with an active set strategy. The computational method is applied to an industrial problem arising in the purification process of zinc hydrometallurgy. Numerical simulation shows that the amount of zinc powder that is needed can be decreased significantly, thus avoiding wastage of resources.

关键词： multiple-time delayed system control parameterization continuous state inequality constraints SQP algorithm

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Restricted second order information for the solution of optimal control problems using control vector parameterization

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JOURNAL OF PROCESS control 2002年第2期12卷 243-255页

作者： Balsa-Canto, E Banga, JR Alonso, AA Vassiliadis, VS Univ Cambridge Dept Chem Engn Cambridge CB2 3RA England Univ Vigo Dept Chem Engn Vigo Spain CSIC Inst Invest Marinas Chem Engn Lab Vigo 36208 Spain

A new scheme using a Truncated Newton algorithm with and exact Hessian-search direction vector product is presented for the solution of optimal control problems. The derivation of formulae for second order parametric sensitivity analysis of differential-algebraic equations is presented, following earlier published work [V.S. Vassiliadis, E. Balsa-Canto, J.R. Banga, Second order sensitivities of general dynamic systems with application to optimal control problems. Chem. Eng. Sci. 54 (17) (1999) 3851-3860]. An original result in this work is the derivation of Hessian matrix-vector product forms which are shown to have the same computational complexity as the evaluation of first order sensitivities. This result for optimal control Hessian-vector products using control vector parameterization is shown to be a very effective way to solve optimal control problems. It is also noted that this work introduces the use of suitable Truncated Newton solvers which can exploit the exact vector products in using conjugate gradient iterations to converge the Newton equations. Such a solver is the TN algorithm of Nash [(S.G. Nash-Newton type minimization via the Lanczos method. SIAM J. Num. Anal. 21, (1984) 770-778)]. Because no full Hessian update is necessary it is demonstrated that the resulting optimal control solver performs very well for a very large number of degrees of freedom, limited only by the necessity for many right-hand-side calculations in the first and second order sensitivity equations (the Hessian vector product). It is also demonstrated by several case studies that the scheme is capable of starting far from the solution and yet arrive there in almost invariant performance. (C) 2002 Published by Elsevier Science Ltd. All rights reserved.

关键词： second order sensitivities first order sensitivities Hessian-vector products optimal control control parameterization differential-algebraic equations ordinary differential equations truncated Newton methods

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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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