Using SOS and sublevel set volume minimization for estimation of forward reachable sets

Morgan Jones; Matthew M. Peet

doi:10.1016/j.ifacol.2019.12.008

Using SOS and sublevel set volume minimization for estimation of forward reachable sets

Morgan Jones, Matthew M. Peet

Research output: Contribution to journal › Conference article › peer-review

10 Scopus citations

Abstract

In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equations (ODE’s) with either (or both) L₂ or point-wise bounded input disturbances. To make our approximations tight we seek to minimize the volume of our approximation set. Our approach to volume minimization is based on the use of a convex determinant-like objective function. We provide several numerical examples including the Lorenz system and the Van der Pol oscillator.

Original language	English (US)
Pages (from-to)	484-489
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	52
Issue number	16
DOIs	https://doi.org/10.1016/j.ifacol.2019.12.008
State	Published - Sep 2019
Event	11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019 - Vienna, Austria Duration: Sep 4 2019 → Sep 6 2019

Keywords

Convex optimization
Nonlinear analysis
Reachable states
Uncertainty

ASJC Scopus subject areas

Control and Systems Engineering

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10.1016/j.ifacol.2019.12.008

Cite this

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title = "Using SOS and sublevel set volume minimization for estimation of forward reachable sets",

abstract = "In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equations (ODE{\textquoteright}s) with either (or both) L2 or point-wise bounded input disturbances. To make our approximations tight we seek to minimize the volume of our approximation set. Our approach to volume minimization is based on the use of a convex determinant-like objective function. We provide several numerical examples including the Lorenz system and the Van der Pol oscillator.",

keywords = "Convex optimization, Nonlinear analysis, Reachable states, Uncertainty",

author = "Morgan Jones and Peet, {Matthew M.}",

note = "Funding Information: This research was carried out with the financial support of the NSF Grant CNS-1739990. Publisher Copyright: {\textcopyright} 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.; 11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019 ; Conference date: 04-09-2019 Through 06-09-2019",

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AU - Jones, Morgan

AU - Peet, Matthew M.

N1 - Funding Information: This research was carried out with the financial support of the NSF Grant CNS-1739990. Publisher Copyright: © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

PY - 2019/9

Y1 - 2019/9

N2 - In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equations (ODE’s) with either (or both) L2 or point-wise bounded input disturbances. To make our approximations tight we seek to minimize the volume of our approximation set. Our approach to volume minimization is based on the use of a convex determinant-like objective function. We provide several numerical examples including the Lorenz system and the Van der Pol oscillator.

AB - In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equations (ODE’s) with either (or both) L2 or point-wise bounded input disturbances. To make our approximations tight we seek to minimize the volume of our approximation set. Our approach to volume minimization is based on the use of a convex determinant-like objective function. We provide several numerical examples including the Lorenz system and the Van der Pol oscillator.

KW - Convex optimization

KW - Nonlinear analysis

KW - Reachable states

KW - Uncertainty

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DO - 10.1016/j.ifacol.2019.12.008

M3 - Conference article

AN - SCOPUS:85077457119

SN - 2405-8963

VL - 52

SP - 484

EP - 489

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 16

T2 - 11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019

Y2 - 4 September 2019 through 6 September 2019

ER -

Using SOS and sublevel set volume minimization for estimation of forward reachable sets

Abstract

Keywords

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