Open-loop optimal controller design using variational iteration method

被引:10
作者
Maidi, Ahmed [1 ]
Corriou, J. P. [2 ]
机构
[1] Univ Mouloud MAMMERI, Lab Concept & Conduite Syst Prod, Tizi Ouzou 15000, Algeria
[2] Nancy Univ, Lab React & Genie Proc, UPR CNRS 3349, ENSIC INPL, F-54001 Nancy, France
关键词
Optimal control; Pontryagin's minimum principle; Hamilton-Jacobi; Variational calculus; Lagrange multiplier; Variational iteration method; DIFFERENTIAL-EQUATIONS; OPTIMIZATION PROBLEMS; DYNAMIC OPTIMIZATION; SYSTEMS; CONSTRAINTS;
D O I
10.1016/j.amc.2013.02.075
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This article presents a design approach of a finite-time open-loop optimal controller using Pontryagin's minimum principle. The resulting equations constitute a two-point boundary-value problem, which is generally impossible to solve analytically and, furthermore the numerical solution is difficult to obtain due to the coupled nature of the solutions. In this paper, the variational iteration method is adopted to easily solve Hamilton equations by use of iteration formulas derived from the correction functionals corresponding to Hamilton equations. The proposed approach allows to derive the numerical solution of the optimal control problem but an analytical or approximate expression of the optimal control law can often be obtained as a function of the time variable, depending on the nature of the control problem, which is simple to implement. The different possible forms of control law that can be attained following the proposed design approach are illustrated by four application examples. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码:8632 / 8645
页数:14
相关论文
共 50 条
[41]   Refined variational iteration method through optimal linear operator and Lagrange multiplier: Local/global convergence [J].
Roy, Tapas ;
Maiti, Dilip Kumar .
APPLIED NUMERICAL MATHEMATICS, 2025, 212 :1-28
[42]   A novel capacitive mass sensor using an open-loop controlled microcantilever [J].
Godara, R. K. ;
Sharma, Atul Kumar ;
Joshi, Nishu ;
Joglekar, M. M. .
MICROSYSTEM TECHNOLOGIES-MICRO-AND NANOSYSTEMS-INFORMATION STORAGE AND PROCESSING SYSTEMS, 2020, 26 (09) :2977-2987
[43]   Nonlinear vibration analysis of a Timoshenko beam with concentrated mass using variational iteration method [J].
Torabi, K. ;
Sharifi, D. ;
Ghassabi, M. .
JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING, 2017, 39 (12) :4887-4894
[44]   Analysis of the motion of a rigid rod on a circular surface using interpolated variational iteration method [J].
Coskun, Safa Bozkurt ;
Senturk, Erman ;
Atay, Mehmet Tarik .
SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, 2022, 40 (03) :577-584
[45]   MEAN-FIELD STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS: OPEN-LOOP SOLVABILITIES [J].
Sun, Jingrui .
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2017, 23 (03) :1099-1127
[46]   NECESSARY AND SUFFICIENT CONDITIONS OF OPEN-LOOP AND CLOSED-LOOP SOLVABILITY FOR DELAYED STOCHASTIC LQ OPTIMAL CONTROL PROBLEMS [J].
Meng, Weijun ;
Shi, Jingtao ;
Zhang, Ji-Feng ;
Zhao, Yanlong .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2025, 63 (03) :1736-1767
[47]   Convexified Open-Loop Stochastic Optimal Control for Linear Systems With Log-Concave Disturbances [J].
Sivaramakrishnan, Vignesh ;
Vinod, Abraham P. ;
Oishi, Meeko M. K. .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2024, 69 (02) :1249-1256
[48]   Solving Non-Linear Quadratic Optimal Control Problems By Variational Iteration Method [J].
Zare, R. ;
Farahi, M. H. ;
Izadian, J. .
JOURNAL OF MATHEMATICAL EXTENSION, 2014, 8 (02) :47-57
[49]   Discrete-time robust voltage controller for buck converters based on the coefficient ratio method with open-loop feed-forward control [J].
Yazici, Irfan ;
Yalcin, Faruk .
INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS, 2021, 31 (12)
[50]   SENSITIVITY ANALYSIS AND DESIGN OF AN OPEN-LOOP ACTIVE NORMAL FORCE FOR DRY FRICTION DAMPERS [J].
Wu, Yaguang ;
Fan, Yu ;
Li, Lin ;
Liu, Jiuzhou .
PROCEEDINGS OF THE ASME CONFERENCE ON SMART MATERIALS, ADAPTIVE STRUCTURES AND INTELLIGENT SYSTEMS, 2017, VOL 2, 2017,