Symbolic Models for a Class of Impulsive Systems

Abdalla Swikir (1) , Antoine Girard (2) , Majid Zamani (3, 4)

1 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich
2 L2S - Laboratoire des signaux et systèmes
3 University of Colorado [Boulder]
4 LMU - Ludwig Maximilian University [Munich] = Ludwig Maximilians Universität München

Symbolic models have been used as the basis of a systematic framework to address control design of several classes of hybrid systems with sophisticated control objectives. However, results available in the literature are not concerned with impulsive systems which are an important modeling framework of many applications. In this paper, we provide an approach for constructing symbolic models for a class of impulsive systems possessing some stability properties. We formally relate impulsive systems and their symbolic models using a notion of so-called alternating simulation function. We show that behaviors of the constructed symbolic models are approximately equivalent to those of the impulsive systems. Finally, we illustrate the effectiveness of our results through a case study.

Mots clés: Hybrid systems; Quantized systems; Supervisory control

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique; Systèmes et contrôle [cs.SY]

Abdalla Swikir, Antoine Girard, Majid Zamani. Symbolic Models for a Class of Impulsive Systems. IEEE Control Systems Letters, 2021, 5 (1), pp.247-252. ⟨10.1109/lcsys.2020.3001501⟩. ⟨hal-02861778⟩