Bounded Nash type controls for uncertain linear systems

Marc Jungers (1) , Eugênio Castelan (2) , Edson Roberto de Pieri (2) , Hisham Abou-Kandil (3)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 DAS - Departamento de Automação e Sistemas
3 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

This paper deals with multicriteria controls for systems coping with polytopic uncertainties. The proposed controls are inspired by a Nash strategy for exactly known systems, reformulated as a nonconvex coupling between Semi-Definite Programming problems. The extension to the uncertain case duplicates the Linear Matrix Inequalities for all vertices of the polytope. A new iterative algorithm using Semi-Definite Programming is provided to design bounded Nash type controls for uncertain systems. A numerical example is given to illustrate the design method.

Domaines: Automatique

Marc Jungers, Eugênio Castelan, Edson Roberto de Pieri, Hisham Abou-Kandil. Bounded Nash type controls for uncertain linear systems. Automatica, 2008, 44 (7), pp.1874-1879. ⟨10.1016/j.automatica.2007.10.035⟩. ⟨hal-00197153⟩