Statistical Hypothesis Testing of Controller Implementations Under Timing Uncertainties

Bineet Ghosh, Clara Hobbs, Shengjie Xu, Parasara Sridhar Duggirala, James H. Anderson, P. S. Thiagarajan, Samarjit Chakraborty

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

Software in autonomous systems, owing to performance requirements, is deployed on heterogeneous hardware comprising task specific accelerators, graphical processing units, and multicore processors. But performing timing analysis for safety critical control software tasks with such heterogeneous hardware is becoming increasingly challenging. Consequently, a number of recent papers have addressed the problem of stability analysis of feedback control loops in the presence of timing uncertainties (cf., deadline misses). In this paper, we address a different class of safety properties, viz., whether the system trajectory deviates too much from the nominal trajectory, with the latter computed for the ideal timing behavior. Verifying such quantitative safety properties involves performing a reachability analysis that is computationally intractable, or is too conservative. To alleviate these problems we propose to provide statistical guarantees over behavior of control systems with timing uncertainties. More specifically, we present a Bayesian hypothesis testing method based on Jeffreys's Bayes factor test that estimates deviations from a nominal or ideal behavior. We show that our analysis can provide, with high confidence, tighter estimates of the deviation from nominal behavior than using known reachability based methods. We also illustrate the scalability of our techniques by obtaining bounds in cases where reachability analysis fails to converge, thereby establishing the former's practicality.

Original languageEnglish
Title of host publicationProceedings - 2022 IEEE 28th International Conference on Embedded and Real-Time Computing Systems and Applications, RTCSA 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages11-20
Number of pages10
ISBN (Electronic)9781665453448
DOIs
StatePublished - 2022
Externally publishedYes
Event28th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications, RTCSA 2022 - Taipei, Taiwan, Province of China
Duration: 23 Aug 202225 Aug 2022

Publication series

NameProceedings - 2022 IEEE 28th International Conference on Embedded and Real-Time Computing Systems and Applications, RTCSA 2022

Conference

Conference28th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications, RTCSA 2022
Country/TerritoryTaiwan, Province of China
CityTaipei
Period23/08/2225/08/22

Keywords

  • Control
  • reachability
  • real-time systems
  • safety
  • statistical hypothesis testing
  • weakly-hard systems

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