Abstract
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.
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.
Original language | English |
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Title of host publication | Proceedings Third International Workshop on Hybrid Autonomous Systems (HAS 2013) |
Editors | Luca Bortolussi, Manuela L. Bujorianu, Giordano Pola |
Number of pages | 17 |
Publisher | Open Publishing Association |
Publication date | 2013 |
Pages | 26-42 |
DOIs | |
Publication status | Published - 2013 |
Event | Third International Workshop on Hybrid Autonomous Systems - Rome, Italy Duration: 17 Mar 2013 → … |
Conference
Conference | Third International Workshop on Hybrid Autonomous Systems |
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Country/Territory | Italy |
City | Rome |
Period | 17/03/2013 → … |
Series | Electronic Proceedings in Theoretical Computer Science |
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Volume | 124 |
ISSN | 2075-2180 |