Robust Static Output Feedback Design with Deterministic and Probabilistic Certificates

Denis Arzelier (1) , F. Dabbene (2) , S. Formentin (3) , Dimitri Peaucelle (4) , Luca Zaccarian (5, 4)

1 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
2 Polito - Politecnico di Torino = Polytechnic of Turin
3 POLIMI - Politecnico di Milano [Milan]
4 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
5 Dipartimento di Ingegneria Industriale [Trento]

Static output feedback design for linear plants is well known to be a challenging non-convex problem. The presence of plant uncertainty makes this challenge even harder. In this chapter, we propose a new BMI formulation with S-variables which includes an interesting link between state feedback, output injection , state injection and static output feedback gains in a unified framework. Based on this formulation, the robust design problem is suitably addressed by iterative optimization procedures with either deterministic or probabilistic viewpoints exploiting the fact that Lyapunov certificates are separated from the control gain design variables. The deterministic approach is for affine polytopic systems. The proba-bilistic approach requires no assumption on the uncertain system and is based on the Scenario with Certificates (SwC) method which was recently proposed to address certain static anti-windup design problems. Numerical results illustrate the effectiveness of the approach in both deterministic and stochastic cases.

Domaines: Automatique / Robotique

Denis Arzelier, F. Dabbene, S. Formentin, Dimitri Peaucelle, Luca Zaccarian. Robust Static Output Feedback Design with Deterministic and Probabilistic Certificates. Uncertainty in Networked Systems: In Honor of Roberto Tempo, Springer, pp.121-148, 2018, ⟨10.1007/978-3-030-04630-9_3⟩. ⟨hal-01970884⟩