Unconditionnally stable scheme for Riccati equation

François Dubois (1) , Abdelkader Saïdi (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IRMA - Institut de Recherche Mathématique Avancée

We present a numerical scheme for the resolution of matrix Riccati equation used in control problems. The scheme is unconditionnally stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.

Mots clés: control problems; ordinary differential equations; stability

Domaines: Analyse numérique [math.NA]

François Dubois, Abdelkader Saïdi. Unconditionnally stable scheme for Riccati equation. ESAIM: Proceedings, 2000, 8, p. 39-52. ⟨10.1051/proc:2000003⟩. ⟨hal-00558312⟩