Minimax controls for uncertain parabolic systems

Nadir Arada (1) , Maïtine Bergounioux (2) , Jean-Pierre Raymond (1)

1 MIP - Mathématiques pour l'Industrie et la Physique
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We consider systems governed by a nonlinear parabolic equation, with a distributed control and a disturbance in the initial condition. We prove the existence of solutions to a corresponding minimax problem, and we obtain necessary optimality conditions in the form of Pontryagin's principles.

Mots clés: uncertain systems; minimax; semilinear parabolic equations; existence of optimal solutions; necessary optimality conditions; Pontryagin's principle

Domaines: Optimisation et contrôle [math.OC]

Nadir Arada, Maïtine Bergounioux, Jean-Pierre Raymond. Minimax controls for uncertain parabolic systems. SIAM Journal on Control and Optimization, 2000, 38, n° 5, pp. 1481-1500. ⟨hal-00022031⟩