Low-regret control for a fractional wave equation with incomplete data

Advances in Difference Equations

Dumitru Baleanu³  Gisle Mophou⁴  Claire Joseph⁶ 

[1] des Antilles et de la Guyane, Pointe-à-Pitre, France;Department of Mathematics, Faculty of Arts and Sciences, ÇInstitute of Space Sciences, Magurele-Bucharest, Romania;Universitéankaya University, Ankara, Turkey

关键词: Riemann-Liouville fractional derivative;    Caputo fractional derivative;    optimal control;    no-regret control;    low-regret control;   

DOI  :  10.1186/s13662-016-0970-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We investigate in this manuscript an optimal control problem for a fractional wave equation involving the fractional Riemann-Liouville derivative and with missing initial condition. For this purpose, we use the concept of no-regret and low-regret controls. Assuming that the missing datum belongs to a certain space we show the existence and the uniqueness of the low-regret control. Besides, its convergence to the no-regret control is discussed together with the optimality system describing the no-regret control.

【 授权许可】

CC BY