OPTIMAL CONTROL WITH FINAL OBSERVATION OF A FRACTIONAL DIFFUSION WAVE EQUATION

Gisèle Mophou (1) , C. Joseph (1)

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

We consider a controlled fractional diffusion wave equation involving Riemann-Liouville fractional derivative or order α ∈ (1, 2). First we prove by means of eigenfunction expansions the existence of solutions to such equations. Then we show that we can approach the fractional integral of order 2 − α of the state at final time by a desired state by acting on the control. Using the first order Euler-Lagrange optimality, we obtain the characterization of the optimal control.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Gisèle Mophou, C. Joseph. OPTIMAL CONTROL WITH FINAL OBSERVATION OF A FRACTIONAL DIFFUSION WAVE EQUATION. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 2016. ⟨hal-02548503⟩