检索结果-内蒙古大学图书馆

A control parameterization method for solving combined fractional optimal parameter selection and optimal control problems

引用

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2025年 141卷

作者： Yi, Xiaopeng Gong, Zhaohua Liu, Chongyang Cheong, Huey Tyng Teo, Kok Lay Wang, Song Sunway Univ Sch Math Sci Kuala Lumpur 47500 Malaysia Shandong Technol & Business Univ Sch Math & Informat Sci Yantai 264005 Peoples R China Curtin Univ Sch Elect Engn Comp & Math Sci Perth 6845 Australia

Many real-world decision problems can be naturally modeled as fractional optimal parameter selection and fractional optimal control problems. Therefore, in this paper, we consider a class of combined fractional optimal parameter selection and optimal control problems involving nonlinear fractional systems with Caputo fractional derivatives and subject to canonical equality and inequality constraints. We first approximate this problem by a set of finite-dimensional optimization problems using the control parameterization method, where both the heights of parameterized controls and system parameters are taken as decision variables. We then show that the gradients of the cost and constraint functions with respect to the decision variables can be expressed as the solutions of a series of auxiliary fractional systems, which can be solved together with the original fractional system forward in time, simultaneously. Furthermore, we present a third-order numerical scheme for solving both the original and auxiliary fractional systems. On this basis, a gradient-based optimization algorithm is developed to solve the resulting optimization problems. Finally, we demonstrate the effectiveness and applicability of the developed algorithm through five non-trivial examples, one of which involves the optimal treatment of human immunodeficiency virus.

关键词： Fractional parameter selection Fractional optimal control control parameterization Numerical scheme Numerical optimization

来源：评论

学校读者我要写书评

暂无评论

control parameterization enhancing transform for optimal control of switched systems

引用

MATHEMATICAL AND COMPUTER MODELLING 2006年第11-12期43卷 1393-1403页

作者： Li, R. Teo, K. L. Wong, K. H. Duan, G. R. Curtin Univ Technol Dept Math & Stat Perth WA 6845 Australia Univ Witwatersrand Dept Computat & Appl Math Johannesburg South Africa Harbin Inst Technol Ctr Control Theory & Guidance Technol Harbin Peoples R China

In this paper, a class of optimal switching control problems with prespecified order of the sequence of subsystems is considered, where the switching instants are included in the cost functional. Both the switching instants and the control function are to be chosen such that the cost functional is minimized. Through the discretization of the control space, each control component is approximated by a piecewise constant function. The partition points and the heights of each of these piecewise constant functions are taken as decision varibles. Using the control parameterization enhancing transform, we map both types of switching instants into preassigned knot points via the introduction of an additional control, known as the enhancing control. In this way, we construct a sequence of approximate optimal parameter selection problems with fixed switching time points. We then show that these approximate optimal parameter selection problems are solvable as mathematical programming problems. The convergence analysis of this approximation is investigated. Two examples are solved using the proposed method so as to demonstrate the effectiveness of the method proposed. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： switched systems optimal control computation control parameterization control parameterization enhancing transform

来源：评论

学校读者我要写书评

暂无评论

control parameterization APPROACH TO TIME-DELAY OPTIMAL control PROBLEMS: A SURVEY

引用

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第5期19卷 3750-3783页

作者： Wu, Di Chen, Yin Yu, Changjun Bai, Yanqin Teo, Kok Lay Shanghai Univ Dept Math Shanghai 200444 Peoples R China Sunway Univ Sch Math Sci Petaling Jaya Malaysia

control parameterization technique is an effective method to solve optimal control problems. It works by approximating the control function by piece-wise constant (or linear) function. In this way, the optimal control problems are approximated by optimal parameter selection problems, which can be regarded as finite-dimensional optimization problems, where the control heights and switching times of the piece-wise constant function are taken as the decision variables. They can be solved by using gradient-based optimization methods. For this, it requires the gradient formulas of the objective and constraint functions with respect to the decision variables. There are two methods for deriving the required gradient formulas. The aim of this paper is to survey various numerical methods developed based on control parameterization for solving optimal control problems governed by time-delay systems. Particular focus is on those numerical methods for optimizing switching time points. This is because the process of optimizing the switching time points is much more complicated for optimal control problems with time delays. In addition, we shall also review the computational methods developed based on control parameterization technique for solving two optimal control problems involving more complicated time delays.

关键词： Optimal control time delays control parameterization

来源：评论

学校读者我要写书评

暂无评论

ON THE CORRELATION OF LOCAL COLLOCATION AND control parameterization METHODS

引用

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2024年第7期20卷 2329-2357页

作者： Su, Shuxuan Shao, Mengzhen Yu, Changjun Teo, Kok lay Shanghai Univ Shanghai Peoples R China Sunway Univ Subang Jaya Malaysia

Local collocation and control parameterization are popular computational methods for solving optimal control problems. The local collocation method works by discretizing both the state and control variables, whereas control parameterization method involves only discretizing the control variable. Despite the extensive development of both approaches over decades, to date, a comprehensive comparison between the two methods hasn't been conducted. In this paper, we establish a set of valid comparison criteria to be used for the comparison of these two approaches. Then, the numerical mechanisms behind both methods are examined and analyzed according to these criteria. Five examples are solved, and the effectiveness of these two methods is compared based on the numerical solutions obtained.

关键词： Optimal control direct collocation control parameterization Runge-Kutta discretization

来源：评论

学校读者我要写书评

暂无评论

Fast control parameterization optimal control with improved Polak-Ribiere-Polyak conjugate gradient implementation for industrial dynamic processes

引用

ISA TRANSACTIONS 2022年 123卷 188-199页

作者： Liu, Ping Hu, Qingquan Li, Lei Liu, Mingjie Chen, Xiaolei Piao, Changhao Liu, Xinggao Chongqing Univ Posts & Telecommun Coll Automation Chongqing 400065 Peoples R China Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol Hangzhou 310027 Peoples R China

This paper proposes a fast control parameterization optimal control algorithm for industrial dynamic process with constraints. Derived from the frame of control variable parameterization (CVP) technique, the proposed method combines an efficient gradient computation strategy with an improved nonlinear optimization computation approach to overcome the challenge of computation efficiency caused by gradients and bounds in optimal control problems. Firstly, a fast gradient computation method based on the costate system of Hamiltonian function is developed to decrease the computational expense of gradients by employing approximate treatments and numerical integration strategy. Then, a trigonometric function transformation scheme is presented to tackle the boundary constraints so that the original optimal control problem is further converted into an unconstrained one. On this basis, an improved restricted Polak-Ribiere-Polyak (PRP) conjugate gradient approach is introduced to solve the nonlinear optimization problem by using conjugate gradient iterations and strong Wolfe line search. Meanwhile, to enhance the convergence, a restricting condition is imposed in strong Wolfe line search to create iteration step-length. Finally, the proposed algorithm is implemented on three dynamic processes. The detailed comparison among the classical CVP method, literature results and the proposed method are carried out. Simulation studies show that the proposed fast approach averagely saves more than 90% computation time in contrast to the classical CVP method, demonstrating the effectiveness of the proposed fast optimal control approach.(c) 2021 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： control parameterization Optimal control PRP conjugate gradient method Fast computation Dynamic processes

来源：评论

学校读者我要写书评

暂无评论

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

引用

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

来源：评论

学校读者我要写书评

暂无评论

Adaptive control parameterization method by density functions for optimal control problems

引用

IMA JOURNAL OF MATHEMATICAL control AND INFORMATION 2020年第2期37卷 497-512页

作者： Ejlali, Nastaran Hosseini, Seyed Mohammad Tarbiat Modares Univ Dept Appl Math POB 14115-175 Tehran Iran

This paper proposes an efficient adaptive control parameterization method for solving optimal control problems. In this method, mesh density functions are used to generate mesh points. In the first step, the problem is solved by control parameterization on uniform mesh points. Then at each step, the approximate control obtained from the previous step is applied to construct a mesh density function, and consequently a new adapted set of mesh points. Several numerical examples are included to demonstrate that the adaptive control parameterization method is more accurate than a uniform control parameterization one.

关键词： optimal control problems inequality constraints control parameterization adaptive mesh refinement

来源：评论

学校读者我要写书评

暂无评论

Unified control parameterization Approach for Finite-Horizon Feedback control With Trajectory Shaping

引用

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2022年第5期58卷 4782-4795页

作者： Cho, Namhoon Park, Jongho Kim, Youdan Shin, Hyo-Sang Cranfield Univ Ctr Autonomous & Cyber Phys Syst Cranfield MK43 0AL Beds England Ajou Univ Dept Mil Digital Convergence Suwon 16499 South Korea Ajou Univ Dept AI Convergence Network Suwon 16499 South Korea Seoul Natl Univ Dept Aerosp Engn Inst Adv Aerosp Technol Seoul 08826 South Korea

This article presents control parameterization as a unifying framework for designing a linear feedback control law that achieves the finite-time transfer of output as well as trajectory shaping. Representing control input as a linear combination of independent basis functions allows wide variability in the resultant feedback control laws through the selection of the number and types of basis functions. Given an array of basis functions that meets the trajectory shaping necessities, the unified design approach proceeds with the determination of the coefficients so that the predicted trajectory attains the desired output at the final time. The input evaluated with the coefficients found at each instance essentially turns out to be a linear state feedback policy with an additional feedforward term and time-dependent gains, which is appropriate for practical use. The unified control parameterization approach lends itself well to missile guidance applications with the expandability and direct trajectory shaping capability that it provides. To emphasize the expandability of the framework, this study revisits the trajectory shaping guidance laws from the control parameterization viewpoint and shows how the notion of specifying input basis functions not only generalizes various existing methods but also enables further extensions. Furthermore, an application to integrated guidance and control illustrates the strength of the design process in handling the shaping requirements more directly through the construction of appropriate basis.

关键词： Trajectory Convergence Time-varying systems Missile guidance Feedback control Tuning State feedback Basis function control parameterization missile guidance terminal control trajectory shaping

来源：评论

学校读者我要写书评

暂无评论

A control parameterization Method to Solve the Fractional-Order Optimal control Problem

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2020年第1期187卷 234-247页

作者： Mu, Pan Wang, Lei Liu, Chongyang Dalian Univ Technol Sch Math Sci Dalian Peoples R China Shandong Inst Business & Technol Sch Math & Informat Sci Yantai Peoples R China Curtin Univ Dept Math & Stat Perth WA Australia

This paper considers a class of fractional optimal control problems with canonical equality and inequality constraints. A fractional derivative in the dynamic system is defined in the Caputo sense. Using the control parameterization method, we approximate fractional optimal control problems by a sequence of finite-dimensional optimization problems. We then present the gradient formulae by introducing some auxiliary fractional systems. On this basis, a gradient-based optimization is developed to solve the fractional optimal control problems. Finally, a numerical example is used to test the proposed method.

关键词： Fractional optimal control control parameterization Gradient formula Auxiliary system

来源：评论

学校读者我要写书评

暂无评论

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

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

引用

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

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：