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[HNP+11] E. M. Hahn, G. Norman, D. Parker, B. Wachter and L. Zhang. Game-based Abstraction and Controller Synthesis for Probabilistic Hybrid Systems. In Proc. 8th International Conference on Quantitative Evaluation of SysTems (QEST'11), pages 69-78, IEEE CS Press. September 2011. [pdf] [bib]
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Abstract. We consider a class of hybrid systems that involve random phenomena, in addition to discrete and continuous behaviour. Examples of such systems include wireless sensing and control applications. We propose and compare two abstraction techniques for this class of models, which yield lower and upper bounds on the optimal probability of reaching a particular class of states. We also demonstrate the applicability of these abstraction techniques to the computation of long-run average reward properties and the synthesis of controllers. The first of the two abstractions yields more precise information, while the second is easier to construct. For the latter, we demonstrate how existing solvers for hybrid systems can be leveraged to perform the computation.