The Maximum Principle for Optimal Control Problems with State Constraints by R.V. Gamkrelidze: Revisited

被引：0

作者：

A. V. Arutyunov

D. Y. Karamzin

F. L. Pereira

机构：

[1] Peoples’ Friendship University of Russia,Dorodnicyn Computing Centre

[2] Russian Academy of Sciences,Faculty of Engineering, University of Porto

[3] University of Porto,undefined

[4] Institute for Systems & Robotics,undefined

来源：

Journal of Optimization Theory and Applications | 2011年 / 149卷

关键词：

Optimal control; Maximum principle; State constraints;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A maximum principle in the form given by R.V. Gamkrelidze is obtained, although without a priori regularity assumptions to be satisfied by the optimal trajectory. After its formulation and proof, we propose various regularity concepts that guarantee, in one sense or another, the nondegeneracy of the maximum principle. Finally, we show how the already known first-order necessary conditions can be deduced from the proposed theorem.

引用

页码：474 / 493

页数：19

共 13 条

[1] Gamkrelidze R.V.(1959)Time-optimal process with bounded phase coordinates Dokl. Akad. Nauk SSSR 125 475-478
[2] Gamkrelidze R.V.(1960)Optimal control processes under bounded phase coordinates Izv. Akad. Nauk SSSR Math. 24 315-356
[3] Dubovitskii A.Ya.(1963)Extremum problems under constraints Dokl. Akad. Nauk SSSR 149 759-762
[4] Milyutin A.A.(1984)The maximum principle in the problem with state constraints Izv. Akad. Nauk SSSR. Ser. Tech. Cybern. 4 60-68
[5] Arutyunov A.V.(1985)The necessary conditions for optimality the problem with state constraints Dokl. Akad. Nauk SSSR 280 1033-1037
[6] Tynyanskii N.T.(1985)Necessary conditions for a strong minimum in optimal control problems with degeneracy of the end-point and phase constraints Usp. Mat. Nauk 2 175-176
[7] Arutyunov A.V.(1989)To the theory of maximum principle in optimal control with state constraints Dokl. Akad. Nauk SSSR 304 11-14
[8] Dubovitskii A.Ya.(2010)Maximum principle in problems with mixed constraints under weak assumptions of regularity J. Optim. 59 1067-1083
[9] Dubovitskii V.A.(undefined)undefined undefined undefined undefined-undefined
[10] Arutyunov A.V.(undefined)undefined undefined undefined undefined-undefined

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