Abstract
We propose a predictive runtime monitoring approach for linear systems with stochastic disturbances. The goal of the monitor is to decide if there exists a possible sequence of control inputs over a given time horizon to ensure that a safety property is maintained with a sufficiently high probability. We derive an efficient algorithm for performing the predictive monitoring in real time, specifically for linear time invariant (LTI) systems driven by stochastic disturbances. The algorithm implicitly defines a control envelope set such that if the current control input to the system lies in this set, there exists a future strategy over a time horizon consisting of the next N steps to guarantee the safety property of interest. As a result, the proposed monitor is oblivious of the actual controller, and therefore, applicable even in the presence of complex control systems including highly adaptive controllers. Furthermore, we apply our proposed approach to monitor whether a UAV will respect a “geofence” defined by a geographical region over which the vehicle may operate. To achieve this, we construct a data-driven linear model of the UAVs dynamics, while carefully modeling the uncertainties due to wind, GPS errors and modeling errors as time-varying disturbances. Using realistic data obtained from flight tests, we demonstrate the advantages and drawbacks of the predictive monitoring approach.
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Acknowledgements
We are grateful to Drs. Jyotirmoy Deshmukh and Derek Kingston for valuable discussions. This work was funded in part by the US National Science Foundation (NSF) under award number 1815983, the US Airforce Research Laboratory and the NSF-IUCRC Center for Unmanned Aerial Systems (C-UAS). All ideas and opinions expressed here are those of the authors and do not necessarily represent those of NSF, AFRL or C-UAS.
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Yoon, H., Chou, Y., Chen, X., Frew, E., Sankaranarayanan, S. (2019). Predictive Runtime Monitoring for Linear Stochastic Systems and Applications to Geofence Enforcement for UAVs. In: Finkbeiner, B., Mariani, L. (eds) Runtime Verification. RV 2019. Lecture Notes in Computer Science(), vol 11757. Springer, Cham. https://doi.org/10.1007/978-3-030-32079-9_20
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