Open-Loop Stackelberg Strategy for Linear-Quadratic games via Matrix Pencil Approach

Marc Jungers (1) , Hisham Abou-Kandil (2) , Cristian Oara (3) , Radu Stefan (3)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie
3 Faculty of Automatic Control and Computers

This paper deals with solving non-symmetric algebraic Riccati systems (NARS) and non-symmetric algebraic Riccati equations (NARE), from Stackelberg strategy with an open-loop information structure applied on linear-quadratic games. A matrix pencil method is chosen for its theoretical and numerical eciency. The main result provides a one-to-one correspondance between disconjugate proper deflating subspaces of a characteristic matrix pencil and the solutions of NARS and NARE. It is shown that this approach is more relevant than ones in the literature, because classical assumptions of some matrix invertibility could be avoided.

Mots clés: Game Theory; Open-Loop Stackelberg Strategy; Matrix Pencils

Domaines: Automatique / Robotique

Marc Jungers, Hisham Abou-Kandil, Cristian Oara, Radu Stefan. Open-Loop Stackelberg Strategy for Linear-Quadratic games via Matrix Pencil Approach. IFAC Workshop on Control Applications of Optimisation, CAO'09, May 2009, Jyväskylä, Finland. pp.CDROM. ⟨hal-00408588⟩