### Abstract

Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates verification that the system does in fact satisfy those requirements at all possible operating conditions. While ana- lytical proof-based techniques and finite abstractions can be used to provably verify the closed-loop system’s response at different operating conditions, they often produce con- servative approximations due to restrictive assumptions and are dificult to construct in many applications. In contrast, popular statistical verification techniques relax the restric- tions and instead rely upon simulations to construct statistical or probabilistic guarantees. This work presents a data-driven statistical verification procedure that instead constructs statistical learning models from simulated training data to separate the set of possible perturbations into “safe” and “unsafe” subsets. Binary evaluations of closed-loop system requirement satisfaction at various realizations of the uncertainties are obtained through temporal logic robustness metrics, which are then used to construct predictive models of requirement satisfaction over the full set of possible uncertainties. As the accuracy of these predictive statistical models is inherently coupled to the quality of the training data, an active learning algorithm selects additional sample points in order to maximize the expected change in the data-driven model and thus, indirectly, minimize the prediction er- ror. Various case studies demonstrate the closed-loop verification procedure and highlight improvements in prediction error over both existing analytical and statistical verification techniques.

Original language | English (US) |
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Title of host publication | AIAA Guidance, Navigation, and Control |

Publisher | American Institute of Aeronautics and Astronautics Inc, AIAA |

Edition | 210039 |

ISBN (Print) | 9781624105265 |

DOIs | |

State | Published - Jan 1 2018 |

Event | AIAA Guidance, Navigation, and Control Conference, 2018 - Kissimmee, United States Duration: Jan 8 2018 → Jan 12 2018 |

### Publication series

Name | AIAA Guidance, Navigation, and Control Conference, 2018 |
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Number | 210039 |

### Other

Other | AIAA Guidance, Navigation, and Control Conference, 2018 |
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Country | United States |

City | Kissimmee |

Period | 1/8/18 → 1/12/18 |

### Fingerprint

### ASJC Scopus subject areas

- Aerospace Engineering
- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*AIAA Guidance, Navigation, and Control*(210039 ed.). (AIAA Guidance, Navigation, and Control Conference, 2018; No. 210039). American Institute of Aeronautics and Astronautics Inc, AIAA. https://doi.org/10.2514/6.2018-1107

**Active sampling-based binary verification of dynamical systems.** / Quindlen, John F.; Topcu, Ufuk; Chowdhary, Girish; How, Jonathan P.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AIAA Guidance, Navigation, and Control.*210039 edn, AIAA Guidance, Navigation, and Control Conference, 2018, no. 210039, American Institute of Aeronautics and Astronautics Inc, AIAA, AIAA Guidance, Navigation, and Control Conference, 2018, Kissimmee, United States, 1/8/18. https://doi.org/10.2514/6.2018-1107

}

TY - GEN

T1 - Active sampling-based binary verification of dynamical systems

AU - Quindlen, John F.

AU - Topcu, Ufuk

AU - Chowdhary, Girish

AU - How, Jonathan P.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates verification that the system does in fact satisfy those requirements at all possible operating conditions. While ana- lytical proof-based techniques and finite abstractions can be used to provably verify the closed-loop system’s response at different operating conditions, they often produce con- servative approximations due to restrictive assumptions and are dificult to construct in many applications. In contrast, popular statistical verification techniques relax the restric- tions and instead rely upon simulations to construct statistical or probabilistic guarantees. This work presents a data-driven statistical verification procedure that instead constructs statistical learning models from simulated training data to separate the set of possible perturbations into “safe” and “unsafe” subsets. Binary evaluations of closed-loop system requirement satisfaction at various realizations of the uncertainties are obtained through temporal logic robustness metrics, which are then used to construct predictive models of requirement satisfaction over the full set of possible uncertainties. As the accuracy of these predictive statistical models is inherently coupled to the quality of the training data, an active learning algorithm selects additional sample points in order to maximize the expected change in the data-driven model and thus, indirectly, minimize the prediction er- ror. Various case studies demonstrate the closed-loop verification procedure and highlight improvements in prediction error over both existing analytical and statistical verification techniques.

AB - Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates verification that the system does in fact satisfy those requirements at all possible operating conditions. While ana- lytical proof-based techniques and finite abstractions can be used to provably verify the closed-loop system’s response at different operating conditions, they often produce con- servative approximations due to restrictive assumptions and are dificult to construct in many applications. In contrast, popular statistical verification techniques relax the restric- tions and instead rely upon simulations to construct statistical or probabilistic guarantees. This work presents a data-driven statistical verification procedure that instead constructs statistical learning models from simulated training data to separate the set of possible perturbations into “safe” and “unsafe” subsets. Binary evaluations of closed-loop system requirement satisfaction at various realizations of the uncertainties are obtained through temporal logic robustness metrics, which are then used to construct predictive models of requirement satisfaction over the full set of possible uncertainties. As the accuracy of these predictive statistical models is inherently coupled to the quality of the training data, an active learning algorithm selects additional sample points in order to maximize the expected change in the data-driven model and thus, indirectly, minimize the prediction er- ror. Various case studies demonstrate the closed-loop verification procedure and highlight improvements in prediction error over both existing analytical and statistical verification techniques.

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UR - http://www.scopus.com/inward/citedby.url?scp=85044572982&partnerID=8YFLogxK

U2 - 10.2514/6.2018-1107

DO - 10.2514/6.2018-1107

M3 - Conference contribution

AN - SCOPUS:85044572982

SN - 9781624105265

T3 - AIAA Guidance, Navigation, and Control Conference, 2018

BT - AIAA Guidance, Navigation, and Control

PB - American Institute of Aeronautics and Astronautics Inc, AIAA

ER -