Index-2 hybrid DAE: a case study with well-posedness and numerical analysis. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Rocca, Alexandre; Acary, Vincent; Brogliato, Bernard
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 1888
• Page End: 1893
• Publication Date: 2020
• Subjects: Hybrid Systems -- ODE -- DAE -- Nonsmooth Dynamical Systems -- Linear Complementarity Systems -- Time-Stepping Scheme -- Euler Method; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.2575
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this work, we study differential algebraic equations with constraints defined in a piecewise manner using a conditional statement. Such models classically appear in systems where constraints can evolve in a very small time frame compared to the observed time scale. The use of conditional statements or hybrid automata is a powerful way to describe such systems and are, in general, well suited to simulation with event driven numerical schemes. However, such methods are often subject to chattering at mode switch in presence of sliding modes, or can result in Zeno behaviours. In contrast, the representation of such systems using differential inclusions and method from non-smooth dynamics are often closer to the physical theory but may be harder to interpret. Associated time-stepping numerical methods have been extensively used in mechanical modelling with success and then extended to other fields such as electronics and system biology. In a similar manner to the previous application of non-smooth methods to the simulation of piecewise linear ODEs, non-smooth event-capturing numerical schemes are applied to piecewise linear DAEs. In particular, the detailed study of a 2-D dynamical system of index-2 with a switching constraint using set-valued operators, is presented.