Turnpike solutions of optimal control problems

被引:0
作者
Quang N.M. [1 ]
Ukhin M.Yu. [2 ]
机构
[1] East Chinese Pedagogical University, Shanghai
[2] Institute of Program Systems, Russian Academy of Sciences, Pereslavl-Zalesskii
来源
Autom. Remote Control | 2006年 / 6卷 / 880-886期
基金
俄罗斯基础研究基金会;
关键词
02.30.Yy;
D O I
10.1134/S000511790606004X
中图分类号
学科分类号
摘要
Minimizing sequences for degenerate optimal control problems are constructed from turnpike solutions. Two variational approximation schemes for the turnpike solution are described: the first is a direct improvement of the simple approximation of piecewise-continuous turnpikes by the solutions of the initial differential system and the second consists of constructing an approximate optimal control in the neighborhood of a turnpike by a parametric curve in the state space. Since a sequence of state-linear feedback controls with variable coefficients is generated in both variants, turnpikes can be easily realized in practice. © Pleiades Publishing, Inc., 2006.
引用
收藏
页码:880 / 886
页数:6
相关论文
共 12 条
[1]  
Gurman V.I., Vyrozhdennye Zadachi Optimal'nogo Upravleniya (Degenerate Optimal Control Problems), (1977)
[2]  
Krotov V.F., Gurman V.I., Metody i Zadachi Optimal'nogo Upravleniya (Methods and Problems of Optimal Control), (1973)
[3]  
Gurman V.I., Printsip Rasshireniya v Zadachakh Optimal'nogo Upravleniya (The Extension Principle in Optimal Control Problems), (1997)
[4]  
Gurman V.I., Turnpike solutions in the procedures seeking optimal controls, Avtom. Telemekh., 3, pp. 61-71, (2003)
[5]  
Gurman V.I., Ukhin M.Yu., The Extension Principle in Control Problems. Constructive Methods and Applied Problems, (2005)
[6]  
Tikhonov A.N., Arsenin V.Ya., Metody Resheniya Nekorrektnykh Zadach (Solution Methods for Ill-defined Problems), (1986)
[7]  
Vasil'eva A.B., Butuzov V.F., Asimptoticheskie Metody v Teorii Singulyarnykh Vozmushchenii (Asymptotic Methods in Singular Perturbation Theory), (1990)
[8]  
Baturin V.A., Urbanovich D.E., Priblizhennye Metody Optimal'nogo Upravleniya, Osnovannye Na Printsipe Rasshireniya (Approximate Optimal Control Methods Based on the Extension Principle), (1997)
[9]  
Gaishun I.V., Vpolne Razreshimye Mnogomernye Differentaial'nye Uravneniya (Completely Solvable Multidimensional Differential Equations), (1983)
[10]  
Dmitriev M.G., Ni Min Quang, Contrast structures in a simple vector variational problem and their asymptotec behavior, Avtom. Telemekh., 5, pp. 41-52, (1998)