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

Dumitru Baleanu (1) , Claire Joseph (2) , Gisèle Mophou (2)

1 Çankaya University
2 LAMIA - Laboratoire de Mathématiques Informatique et Applications [UR1_1]

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.

Mots clés: Riemann-Liouville fractional derivative; Caputo fractional derivative; optimal control; no-regret control; low-regret control

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Dumitru Baleanu, Claire Joseph, Gisèle Mophou. Low-regret control for a fractional wave equation with incomplete data. Advances in Difference Equations, 2016, ⟨10.1186/s13662-016-0970-8⟩. ⟨hal-02548520⟩