Complete abstractions of dynamical systems by timed automata

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• 作者：Christoffer Sloth ; Rafael Wisniewski
• 关键词：Abstraction ; Verification ; Reachability ; Timed automata
• 刊名：Nonlinear Analysis: Hybrid Systems
• 出版年：2013
• 出版时间：February, 2013
• 年：2013
• 卷：7
• 期：1
• 页码：80-100
• 全文大小：410 K

文摘

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.