Adaptive control design with S-variable LMI approach for robustness and L2 performance

Dimitri Peaucelle (1) , Harmonie Leduc (1)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

Matrix inequality based results are proposed for the design of direct adaptive control. The focus is on guaranteeing robustness of the closed-loop when facing both structured parametric uncertainties and input disturbances. Results apply to systems in descriptor form with polytopic uncertainties and readily extend to systems rational in the uncertain parameters. The exposed methodology is an extension of previous studies started in cooperation with Alexander L. Fradkov. These studies aim at applying up-to-date linear robust control tools for passivity-based adaptive control. The paper contributes to this framework with new parameter-dependent Lyapunov functions and new degrees of freedom in the adaptive laws offering the possibility to design controllers with improved closed-loop performances.

Mots clés: Uncertain polytopic systems; L2 performance; Practical stability; Adaptive control; LMIs; Descriptor systems

Domaines: Automatique

Dimitri Peaucelle, Harmonie Leduc. Adaptive control design with S-variable LMI approach for robustness and L2 performance. International Journal of Control, 2020, 93 (2), pp.194-203. ⟨10.1080/00207179.2018.1554907⟩. ⟨hal-01960048⟩