### Abstract

The automatic analysis of transient properties of nonlinear dynamical systems is a challenging problem. The problem is even more challenging when complex state-space and timing requirements must be satisfied by the system. Such complex requirements can be captured by Metric Temporal Logic (MTL) specifications. The problem of finding system behaviors that do not satisfy an MTL specification is referred to as MTL falsification. This paper presents an approach for improving stochastic MTL falsification methods by performing local search in the set of initial conditions. In particular, MTL robustness quantifies how correct or wrong is a system trajectory with respect to an MTL specification. Positive values indicate satisfaction of the property while negative values indicate falsification. A stochastic falsification method attempts to minimize the system's robustness with respect to the MTL property. Given some arbitrary initial state, this paper presents a method to compute a descent direction in the set of initial conditions, such that the new system trajectory gets closer to the unsafe set of behaviors. This technique can be iterated in order to converge to a local minimum of the robustness landscape. The paper demonstrates the applicability of the method on some challenging nonlinear systems from the literature.

Original language | English (US) |
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Title of host publication | Proceedings of the American Control Conference |

Pages | 4405-4410 |

Number of pages | 6 |

State | Published - 2013 |

Event | 2013 1st American Control Conference, ACC 2013 - Washington, DC, United States Duration: Jun 17 2013 → Jun 19 2013 |

### Other

Other | 2013 1st American Control Conference, ACC 2013 |
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Country | United States |

City | Washington, DC |

Period | 6/17/13 → 6/19/13 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the American Control Conference*(pp. 4405-4410). [6580518]

**Computing descent direction of MTL robustness for non-linear systems.** / Abbas, Houssam; Fainekos, Georgios.

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

*Proceedings of the American Control Conference.*, 6580518, pp. 4405-4410, 2013 1st American Control Conference, ACC 2013, Washington, DC, United States, 6/17/13.

}

TY - GEN

T1 - Computing descent direction of MTL robustness for non-linear systems

AU - Abbas, Houssam

AU - Fainekos, Georgios

PY - 2013

Y1 - 2013

N2 - The automatic analysis of transient properties of nonlinear dynamical systems is a challenging problem. The problem is even more challenging when complex state-space and timing requirements must be satisfied by the system. Such complex requirements can be captured by Metric Temporal Logic (MTL) specifications. The problem of finding system behaviors that do not satisfy an MTL specification is referred to as MTL falsification. This paper presents an approach for improving stochastic MTL falsification methods by performing local search in the set of initial conditions. In particular, MTL robustness quantifies how correct or wrong is a system trajectory with respect to an MTL specification. Positive values indicate satisfaction of the property while negative values indicate falsification. A stochastic falsification method attempts to minimize the system's robustness with respect to the MTL property. Given some arbitrary initial state, this paper presents a method to compute a descent direction in the set of initial conditions, such that the new system trajectory gets closer to the unsafe set of behaviors. This technique can be iterated in order to converge to a local minimum of the robustness landscape. The paper demonstrates the applicability of the method on some challenging nonlinear systems from the literature.

AB - The automatic analysis of transient properties of nonlinear dynamical systems is a challenging problem. The problem is even more challenging when complex state-space and timing requirements must be satisfied by the system. Such complex requirements can be captured by Metric Temporal Logic (MTL) specifications. The problem of finding system behaviors that do not satisfy an MTL specification is referred to as MTL falsification. This paper presents an approach for improving stochastic MTL falsification methods by performing local search in the set of initial conditions. In particular, MTL robustness quantifies how correct or wrong is a system trajectory with respect to an MTL specification. Positive values indicate satisfaction of the property while negative values indicate falsification. A stochastic falsification method attempts to minimize the system's robustness with respect to the MTL property. Given some arbitrary initial state, this paper presents a method to compute a descent direction in the set of initial conditions, such that the new system trajectory gets closer to the unsafe set of behaviors. This technique can be iterated in order to converge to a local minimum of the robustness landscape. The paper demonstrates the applicability of the method on some challenging nonlinear systems from the literature.

UR - http://www.scopus.com/inward/record.url?scp=84883502317&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883502317&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781479901777

SP - 4405

EP - 4410

BT - Proceedings of the American Control Conference

ER -