Differential-Algebraic Inclusions with Maximal Monotone Operators

Kanat Camlibel (1) , Luigi Iannelli (2) , Aneel Tanwani (3) , Stephan Trenn (4)

1 Bernoulli Institute for Mathematics and Computer Science and Artificial Intelligence
2 Dipartimento di Ingegneria [Benevento]
3 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
4 TU Kaiserslautern - Technical University of Kaiserslautern

The term differential-algebraic inclusions (DAIs) not only describes the dynamical relations using set-valued mappings, but also includes the static algebraic inclusions, and this paper considers the problem of existence of solutions for a class of such dynamical systems. The existence of solutions is proved using the tools from the theory of maximal monotone operators. The class of solutions that we study in the paper have the property that, instead of the whole state, only certain component of the solution is absolutely continuous and unique. This framework, in particular, is useful for studying passive differential-algebraic equations (DAEs) coupled with maximal monotone relations. Certain class of irregular DAEs are also covered within the proposed general framework. Applications from electrical circuits are included to provide a practical motivation.

Domaines: Systèmes et contrôle [cs.SY]; Automatique; Optimisation et contrôle [math.OC]; Systèmes dynamiques [math.DS]

Kanat Camlibel, Luigi Iannelli, Aneel Tanwani, Stephan Trenn. Differential-Algebraic Inclusions with Maximal Monotone Operators. 55th IEEE Conference on Decision and Control, Dec 2016, Las Vegas, United States. ⟨hal-01366071⟩