A Mori-Zwanzig and MITL based approach to statistical verification of continuous-time dynamical systems
Y. Wang, N. Roohi, M. West, M. Viswanathan, and G. E. Dullerud
in Proceedings of the 5th IFAC Workshop on Analysis and Design of Hybrid Systems (ADHS '15), 2015.
In this work, we introduce a framework for the statistical verification of Metric Interval Temporal Logic (MITL) formulas on continuous-time dynamical systems. By considering the continuous-time Markov process associated with the dynamical system, we apply the Mori-Zwanzig method to reduce the original system to a Continuous-Time Markov Chain (CTMC). Accordingly, the MITL formulas on the original system can be reduced to MITL formulas on the CTMC. Furthermore, we propose a statistical verification algorithm for checking the MITL formulas on the CTMC and show that the original MITL formulas on the original system can be checked by this procedure.
Full text: WaRoWeViDu2015b.pdf