Optimal Control for Fractional Diffusion Equations with Incomplete Data

被引：10

作者：

Mophou, Gisele ^{[1
,2
]}

机构：

[1] Univ Antilles Guyane, Lab CEREGMIA, Campus Fouillole, F-97159 Pointe A Pitre, Guadeloupe, France

[2] Univ Ouaga 3S, Lab MAINEGE, 06 BP 10347, Ouagadougou 06, Burkina Faso

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2017年 / 174卷 / 01期

关键词：

No-regret control; Time-fractional differential equation; Incomplete data; Optimality system; Euler-Lagrange formula; NO-REGRET CONTROL; DISTRIBUTED SYSTEMS; SOLUTION SCHEME; FORMULATION; DYNAMICS;

D O I：

10.1007/s10957-015-0817-6

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We are concerned with the optimal control of time-fractional diffusion equations with missing boundary condition. Using the notion of no-regret control and least (or low) regret control developed by Lions, we first prove that the least regret control problem associated with the boundary fractional diffusion equation has a unique solution. Then we show that this solution converges to the no-regret control which we characterize by a singular optimality system.

引用

页码：176 / 196

页数：21

共 39 条

[1] Fractional Optimal Control Problems with Several State and Control Variables
Agrawal, Om P.
Defterli, Ozlem
Baleanu, Dumitru
[J]. JOURNAL OF VIBRATION AND CONTROL, 2010, 16 (13) : 1967 - 1976
[2] A general formulation and solution scheme for fractional optimal control problems
Agrawal, OP
[J]. NONLINEAR DYNAMICS, 2004, 38 (1-4) : 323 - 337
[3] Formulation of Euler-Lagrange equations for fractional variational problems
Agrawal, OP
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 272 (01) : 368 - 379
[4] Spectral analysis of fractional kinetic equations with random data
Anh, VV
Leonenko, NN
[J]. JOURNAL OF STATISTICAL PHYSICS, 2001, 104 (5-6) : 1349 - 1387
[5] [Anonymous], 2006, THEORY APPL FRACTION
[6] [Anonymous], 2010, J. Math. Ind.
[7] [Anonymous], 1993, INTRO FRACTIONAL CA
[8] [Anonymous], 1974, The fractional calculus theory and applications of differentiation and integration to arbitrary order, DOI DOI 10.1016/S0076-5392(09)60219-8
[9] [Anonymous], 1999, FRACTIONAL DIFFERENT
[10] [Anonymous], 1968, TRAVAUX RECHERCHES M

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