Robust-to-dynamics linear programming

Amir Ali Ahmad; Oktay Günluk

doi:10.1109/CDC.2015.7403149

Robust-to-dynamics linear programming

Amir Ali Ahmad, Oktay Günluk

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

2 Scopus citations

Abstract

We consider a class of robust optimization problems that we call robust-to-dynamics optimization (RDO). The input to an RDO problem is twofold: (i) a mathematical program (e.g., an LP, SDP, IP, etc.), and (ii) a dynamical system (e.g., a linear, nonlinear, discrete, or continuous dynamics). The objective is to maximize over the set of initial conditions that forever remain feasible under the dynamics. The focus of this paper is on the case where the optimization problem is a linear program and the dynamics are linear. We establish some structural properties of the feasible set and prove that if the linear system is asymptotically stable, then the RDO problem can be solved in polynomial time. We also outline a semidefinite programming based algorithm for providing upper bounds on robust-to-dynamics linear programs.

Original language	English (US)
Title of host publication	54rd IEEE Conference on Decision and Control,CDC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5915-5919
Number of pages	5
ISBN (Electronic)	9781479978861
DOIs	https://doi.org/10.1109/CDC.2015.7403149
State	Published - Feb 8 2015
Event	54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: Dec 15 2015 → Dec 18 2015

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	54th IEEE Conference on Decision and Control, CDC 2015
Country/Territory	Japan
City	Osaka
Period	12/15/15 → 12/18/15

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Keywords

Robust optimization
dynamical systems
linear programming
semidefinite programming

Access to Document

10.1109/CDC.2015.7403149

Cite this

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title = "Robust-to-dynamics linear programming",

abstract = "We consider a class of robust optimization problems that we call robust-to-dynamics optimization (RDO). The input to an RDO problem is twofold: (i) a mathematical program (e.g., an LP, SDP, IP, etc.), and (ii) a dynamical system (e.g., a linear, nonlinear, discrete, or continuous dynamics). The objective is to maximize over the set of initial conditions that forever remain feasible under the dynamics. The focus of this paper is on the case where the optimization problem is a linear program and the dynamics are linear. We establish some structural properties of the feasible set and prove that if the linear system is asymptotically stable, then the RDO problem can be solved in polynomial time. We also outline a semidefinite programming based algorithm for providing upper bounds on robust-to-dynamics linear programs.",

keywords = "Robust optimization, dynamical systems, linear programming, semidefinite programming",

author = "Ahmad, {Amir Ali} and Oktay G{\"u}nluk",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; 54th IEEE Conference on Decision and Control, CDC 2015 ; Conference date: 15-12-2015 Through 18-12-2015",

year = "2015",

month = feb,

day = "8",

doi = "10.1109/CDC.2015.7403149",

language = "English (US)",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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booktitle = "54rd IEEE Conference on Decision and Control,CDC 2015",

address = "United States",

}

Ahmad, AA & Günluk, O 2015, Robust-to-dynamics linear programming. in 54rd IEEE Conference on Decision and Control,CDC 2015., 7403149, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 5915-5919, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 12/15/15. https://doi.org/10.1109/CDC.2015.7403149

TY - GEN

T1 - Robust-to-dynamics linear programming

AU - Ahmad, Amir Ali

AU - Günluk, Oktay

PY - 2015/2/8

Y1 - 2015/2/8

N2 - We consider a class of robust optimization problems that we call robust-to-dynamics optimization (RDO). The input to an RDO problem is twofold: (i) a mathematical program (e.g., an LP, SDP, IP, etc.), and (ii) a dynamical system (e.g., a linear, nonlinear, discrete, or continuous dynamics). The objective is to maximize over the set of initial conditions that forever remain feasible under the dynamics. The focus of this paper is on the case where the optimization problem is a linear program and the dynamics are linear. We establish some structural properties of the feasible set and prove that if the linear system is asymptotically stable, then the RDO problem can be solved in polynomial time. We also outline a semidefinite programming based algorithm for providing upper bounds on robust-to-dynamics linear programs.

AB - We consider a class of robust optimization problems that we call robust-to-dynamics optimization (RDO). The input to an RDO problem is twofold: (i) a mathematical program (e.g., an LP, SDP, IP, etc.), and (ii) a dynamical system (e.g., a linear, nonlinear, discrete, or continuous dynamics). The objective is to maximize over the set of initial conditions that forever remain feasible under the dynamics. The focus of this paper is on the case where the optimization problem is a linear program and the dynamics are linear. We establish some structural properties of the feasible set and prove that if the linear system is asymptotically stable, then the RDO problem can be solved in polynomial time. We also outline a semidefinite programming based algorithm for providing upper bounds on robust-to-dynamics linear programs.

KW - Robust optimization

KW - dynamical systems

KW - linear programming

KW - semidefinite programming

UR - http://www.scopus.com/inward/record.url?scp=84962033050&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962033050&partnerID=8YFLogxK

U2 - 10.1109/CDC.2015.7403149

DO - 10.1109/CDC.2015.7403149

M3 - Conference contribution

AN - SCOPUS:84962033050

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5915

EP - 5919

BT - 54rd IEEE Conference on Decision and Control,CDC 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 54th IEEE Conference on Decision and Control, CDC 2015

Y2 - 15 December 2015 through 18 December 2015

ER -

Robust-to-dynamics linear programming

Abstract

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All Science Journal Classification (ASJC) codes

Keywords

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