## 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.

DOI: 10.1016/j.ifacol.2015.11.186

Full text: WaRoWeViDu2015b.pdf