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Solving an identification problem as an impulsive optimal parameter selection problem

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2005年第1-2期50卷 217-229页

作者： Wu, CZ Teo, KL Zhao, Y Yan, WY Zhongshan Univ Dept Math Guangzhou Peoples R China Curtin Univ Technol Dept Math & Stat Perth WA 6845 Australia Curtin Univ Technol Dept Elect & Comp Engn Perth WA 6845 Australia

In this paper, we consider an interesting identification problem where an unknown phenomenon is to be identified by the trajectory of an impulsive differential equation. The system coefficients, the locations of the switching time points, and the heights of the jumps at these time points are to be determined such that the summation of the least square errors of the trajectory of the impulsive system and the phenomenon over the observed time points is minimized. This becomes an interesting dynamical optimization problem. We develop an efficient computational method for solving this dynamical optimization problem. Our approach first is to use the control parameterization enhancing transform to convert this dynamical optimization problem into an equivalent optimal parameter selection problem, where the varying time points are being mapped into fixed time points. Then, the gradient formula of the cost function is derived. Thus, this optimal parameter selection problem can be solved as a mathematical programming problem. For illustration, a numerical example is solved by using the proposed method. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： identification problem control parameterization enhancing transform impulsive system optimal parameter selection problem computational method

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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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OPTIMAL-control COMPUTATION FOR NONLINEAR TIME-LAG SYSTEMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1985年第1期47卷 91-107页

作者： WONG, KH CLEMENTS, DJ TEO, KL UNIV NEW S WALES SCH ELECT ENGN & COMP SCIKENSINGTONNSW 2033AUSTRALIA NATL UNIV SINGAPORE DEPT IND & SYST ENGNSINGAPORE 0511SINGAPORE

In this paper, a computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving nonlinear hereditary systems with linear control constraints... 详细信息

关键词： computational schemes control parameterization linear control constraints nonlinear hereditary systems piecewise constant functions

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A NEW GRADIENT COMPUTATIONAL FORMULA FOR OPTIMAL control PROBLEMS WITH TIME-DELAY

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2022年第4期18卷 2469-2482页

作者： Yu, Changjun Yuan, Lei Su, Shuxuan Shanghai Univ Shanghai 200444 Peoples R China

In this paper, we consider a class of time-delay optimal control problem (TDOCP) with canonical equality and inequality constraints. By applying control parameterization method together with time-scaling transformation, a TDOCP can be readily solved by gradient-based optimization methods. The partial derivative of the cost as well as the constraint functions with respect to the decision variables are obtained by variational approach, which is inefficient when the discretization for the control function is relatively dense. For general optimal control problem without time-delay, co-state approach is an effective way to compute the gradients, however, when time-delay is involved in the dynamic system, the co-state system is not known. In this paper, we derive the co-state system for TDOCP to compute the gradients of the cost and constraints. Numerical results show that the computational efficiency is much higher when compared with the traditional variational approach.

关键词： Time-delay system optimal control co-state system control parameterization time-scaling transformation

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Smoothing spline via optimal control under uncertainty

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APPLIED MATHEMATICAL MODELLING 2018年 58卷 203-216页

作者： Yu, Changjun Wang, Yujing Li, Linna Shanghai Univ Dept Math Shanghai Peoples R China Curtin Univ Dept Math & Stat Perth WA Australia

In this paper, we consider a class of control theoretic spline model, which can be formulated as a linear quadratic optimal control problem. The unknown initial condition and the control are to be chosen optimally such that the output best fits a set of measurement data which are corrupted by noise with crucial knowledge of its distribution. We first transform the uncertain objective function into a deterministic objective function. The solution method is based on the control parameterization technique. We show that the approximate optimal controls obtained from the approximate finite dimensional problems converge to the optimal control of the original control problem in the weak(star) topology of L-infinity([0, T], R-r). Numerical results show that the proposed method is effective. (C) 2017 Published by Elsevier Inc.

关键词： Smoothing spline Optimal control Uncertainty control parameterization

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The approximation for the boundary optimal control problem of Burgers-Fisher equation with constraints

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APPLIED MATHEMATICS AND COMPUTATION 2014年 243卷 889-898页

作者： Yu, Xin Cheng, Rongjun Jiang, Huachen Zhang, Qian Xu, Chao Zhejiang Univ Ningbo Inst Technol Lab Informat & Control Technol Ningbo 315100 Zhejiang Peoples R China 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

This paper deals with the numerical approximation with meshless method for the boundary optimal control problem with some control and state constraints governed by the Burgers-Fisher equation, which is a nonlinear evolution equation and is the prototype model for the reaction, convection and diffusion phenomena arising in many spatial-temporal processes. By making use of the element-free Galerkin (EFG) method, the original optimal control problem is discretized spatially to a semi-discrete optimal control problem governed by a system of nonlinear ordinary differential equations. Then, by using the control parameterization method, the original problem can be reduced to an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problems by using the Sequential Quadratic Programming (SQP) algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Meshless method Boundary optimal control Burgers-Fisher equation State and control constraints control parameterization

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A Hybrid Time-Scaling Transformation for Time-Delay Optimal control Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2016年第3期169卷 876-901页

作者： Yu, Changjun Lin, Qun Loxton, Ryan Teo, Kok Lay Wang, Guoqiang Cent S Univ Changsha Hunan Peoples R China Curtin Univ Perth WA 6845 Australia Shanghai Univ Engn Sci Shanghai Peoples R China

In this paper, we consider a class of nonlinear time-delay optimal control problems with canonical equality and inequality constraints. We propose a new computational approach, which combines the control parameterization technique with a hybrid time-scaling strategy, for solving this class of optimal control problems. The proposed approach involves approximating the control variables by piecewise constant functions, whose heights and switching times are decision variables to be optimized. Then, the resulting problem with varying switching times is transformed, via a new hybrid time-scaling strategy, into an equivalent problem with fixed switching times, which is much preferred for numerical computation. Our new time-scaling strategy is hybrid in the sense that it is related to two coupled time-delay systems-one defined on the original time scale, in which the switching times are variable, the other defined on the new time scale, in which the switching times are fixed. This is different from the conventional time-scaling transformation widely used in the literature, which is not applicable to systems with time-delays. To demonstrate the effectiveness of the proposed approach, we solve four numerical examples. The results show that the costs obtained by our new approach are lower, when compared with those obtained by existing optimal control methods.

关键词： Time-delay Optimal control control parameterization Time-scaling transformation Time-delay control system Computational method for optimal control

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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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A new computational approach for optimal control of switched systems

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2024年第1期2024卷 1-16页

作者： Zhu, Xi Bai, Yanqin Yu, Changjun Teo, Kok Lay Shanghai Univ Dept Math Shanghai Peoples R China Sunway Univ Sch Math Sci Sunway Malaysia

The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples.

关键词： Switched system Optimal control Switching time optimization control parameterization Time-scaling transformation

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Optimal operation processes of discrete-continuous biochemical processes

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COMPUTERS & CHEMICAL ENGINEERING 2000年第2-7期24卷 1167-1173页

作者： Chekhova, E Barton, PI Gorak, A MIT Dept Chem Engn Cambridge MA 02139 USA Univ Dortmund Dept Chem Engn D-44221 Dortmund Germany

Biohemical processes and so-called hybrid biochemical processes, carried out in integrated unit operations such as membrane bioreactors, have found numerous applications in food and pharmaceutical process industries. However, such processes have hardly been investigated comprehensively. Dynamic modeling and especially dynamic optimization attempts were restricted because these unit operations combine continuous and discrete dynamic behavior and contain time and state events. In this paper we present a robust model of a process of high industrial significance, namely citric acid production in a membrane bioreactor, as well as a successful application of control parameterization numerical optimal control techniques to the fed-batch bioreactor and a membrane bioreactor. In order to evaluate the advantages and disadvantages of the design alternatives, the incremental objective function between batch and fed-batch, batch and different operations in a membrane bioreactor was formulated in terms of profit maximization. The determination of the optimal performance for the fed-batch fermenter and membrane bioreactor requires the solution of multiple optimal control problems, namely determining optimal feed and inlet concentration profiles, initial conditions and a production time. We show how the systematic combination of rigorous mathematical modeling: the integration of design and operational decisions and innovative discrete-continuous dynamic optimization techniques allow the generation of optimal designs and operating policies for hybrid biochemical processes that increase the profit of important production processes such as citric acid production. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： optimal operation discrete-continuous biochemical processes citric acid production design alternatives control parameterization membrane bioreactor

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