### Abstract

In this paper, a computationally efficient approach is presented to enable onboard computation of reachability sets for the hypersonic re-entry problem. The main idea is to consider the bounded control variables as random variables and represent the reachability sets as the level sets of the state probability density function. A main advantage of such an approach is that it provide not only the boundary of the reachability set but it also characterizes the probability distribution of state variable due to variation in control input. The computation of state density function due to variation in control input at each time is made tractable by computing desired order statistical moments of state density function at each time. Conjugate Unscented Transform (CUT) algorithm is used to compute the moment generating function. Finally, a prototype model of the hypersonic re-entry problem is considered to show the efficacy and utility of the proposed ideas.

Original language | English (US) |
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Title of host publication | Spaceflight Mechanics 2019 |

Editors | Francesco Topputo, Andrew J. Sinclair, Matthew P. Wilkins, Renato Zanetti |

Publisher | Univelt Inc. |

Pages | 2455-2476 |

Number of pages | 22 |

ISBN (Print) | 9780877036593 |

State | Published - Jan 1 2019 |

Event | 29th AAS/AIAA Space Flight Mechanics Meeting, 2019 - Maui, United States Duration: Jan 13 2019 → Jan 17 2019 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 168 |

ISSN (Print) | 0065-3438 |

### Conference

Conference | 29th AAS/AIAA Space Flight Mechanics Meeting, 2019 |
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Country | United States |

City | Maui |

Period | 1/13/19 → 1/17/19 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Spaceflight Mechanics 2019*(pp. 2455-2476). [AAS 19-468] (Advances in the Astronautical Sciences; Vol. 168). Univelt Inc..

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*Spaceflight Mechanics 2019.*, AAS 19-468, Advances in the Astronautical Sciences, vol. 168, Univelt Inc., pp. 2455-2476, 29th AAS/AIAA Space Flight Mechanics Meeting, 2019, Maui, United States, 1/13/19.

**Stochastic reachability analysis for the hypersonic re-entry problem.** / Jain, Amit; Guého, Damien; Singla, Puneet; Akella, Maruthi.

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

TY - GEN

T1 - Stochastic reachability analysis for the hypersonic re-entry problem

AU - Jain, Amit

AU - Guého, Damien

AU - Singla, Puneet

AU - Akella, Maruthi

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this paper, a computationally efficient approach is presented to enable onboard computation of reachability sets for the hypersonic re-entry problem. The main idea is to consider the bounded control variables as random variables and represent the reachability sets as the level sets of the state probability density function. A main advantage of such an approach is that it provide not only the boundary of the reachability set but it also characterizes the probability distribution of state variable due to variation in control input. The computation of state density function due to variation in control input at each time is made tractable by computing desired order statistical moments of state density function at each time. Conjugate Unscented Transform (CUT) algorithm is used to compute the moment generating function. Finally, a prototype model of the hypersonic re-entry problem is considered to show the efficacy and utility of the proposed ideas.

AB - In this paper, a computationally efficient approach is presented to enable onboard computation of reachability sets for the hypersonic re-entry problem. The main idea is to consider the bounded control variables as random variables and represent the reachability sets as the level sets of the state probability density function. A main advantage of such an approach is that it provide not only the boundary of the reachability set but it also characterizes the probability distribution of state variable due to variation in control input. The computation of state density function due to variation in control input at each time is made tractable by computing desired order statistical moments of state density function at each time. Conjugate Unscented Transform (CUT) algorithm is used to compute the moment generating function. Finally, a prototype model of the hypersonic re-entry problem is considered to show the efficacy and utility of the proposed ideas.

UR - http://www.scopus.com/inward/record.url?scp=85072972537&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072972537&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85072972537

SN - 9780877036593

T3 - Advances in the Astronautical Sciences

SP - 2455

EP - 2476

BT - Spaceflight Mechanics 2019

A2 - Topputo, Francesco

A2 - Sinclair, Andrew J.

A2 - Wilkins, Matthew P.

A2 - Zanetti, Renato

PB - Univelt Inc.

ER -