Luca Bortolussi, Manuela L. Bujorianu, Giordano Pola
1 Aalborg University Space Center, The Faculty of Engineering and Science, Aalborg University, VBN2 Automation & Control, The Faculty of Engineering and Science, Aalborg University, VBN3 Department of Electronic Systems, The Faculty of Engineering and Science, Aalborg University, VBN4 Aalborg U Robotics, The Faculty of Humanities, Aalborg University, VBN5 The Faculty of Engineering and Science, Aalborg University, VBN
This paper addresses the generation of complete abstractions of polynomial dynamical systems by timed automata. For the proposed abstraction, the state space is divided into cells by sublevel sets of functions. We identify a relation between these functions and their directional derivatives along the vector field, which allows the generation of a complete abstraction. To compute the functions that define the subdivision of the state space in an algorithm, we formulate a sum of squares optimization problem. This optimization problem finds the best subdivisioning functions, with respect to the ability to approximate the dynamical system, in a subset of admissible subdivisioning functions.
Electronic Proceedings in Theoretical Computer Science, 2013, p. 26-42
Main Research Area:
Electronic Proceedings in Theoretical Computer Science
Third International Workshop on Hybrid Autonomous Systems, 2013