research-article

On the Polytope Escape Problem for Continuous Linear Dynamical Systems

Authors:

Joao Sousa-Pinto,

James WorrellAuthors Info & Claims

HSCC '17: Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control

Pages 11 - 17

https://doi.org/10.1145/3049797.3049798

Published: 13 April 2017 Publication History

Abstract

The Polytope Escape Problem for continuous linear dynamical systems consists of deciding, given an affine function f:R^d -> R^d and a convex polytope P⊆ R^d, both with rational descriptions, whether there exists an initial point x₀ in P such that the trajectory of the unique solution to the differential equation: ·x(t)=f(x(t)) x 0= x₀ is entirely contained in P. We show that this problem is reducible in polynomial time to the decision version of linear programming with real algebraic coefficients. The latter is a special case of the decision problem for the existential theory of real closed fields, which is known to lie between NP and PSPACE. Our algorithm makes use of spectral techniques and relies, among others, on tools from Diophantine approximation.

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Cited By

Karimov TLefaucheux EOuaknine JPurser DVaronka AWhiteland MWorrell J(2022)What’s decidable about linear loops?Proceedings of the ACM on Programming Languages10.1145/34987276:POPL(1-25)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3498727
Akshay SGenest BVyas N(2018)Distribution-based objectives for Markov Decision ProcessesProceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3209108.3209185(36-45)Online publication date: 9-Jul-2018
https://dl.acm.org/doi/10.1145/3209108.3209185
Gan TChen MLi YXia BZhan N(2018)Reachability Analysis for Solvable Dynamical SystemsIEEE Transactions on Automatic Control10.1109/TAC.2017.276378563:7(2003-2018)Online publication date: Jul-2018
https://doi.org/10.1109/TAC.2017.2763785

Index Terms

On the Polytope Escape Problem for Continuous Linear Dynamical Systems
1. Theory of computation
  1. Models of computation
    1. Timed and hybrid models

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cover image ACM Conferences

HSCC '17: Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control

April 2017

288 pages

ISBN:9781450345903

DOI:10.1145/3049797

Program Chairs:
Goran Frehse
University Grenoble Alpes
,
Sayan Mitra
University of Illinois at Urbana Champaign

Copyright © 2017 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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SIGBED: ACM Special Interest Group on Embedded Systems

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Association for Computing Machinery

New York, NY, United States

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Published: 13 April 2017

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European Research Council

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HSCC '17

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HSCC '17: 20th International Conference on Hybrid Systems: Computation and Control

April 18 - 20, 2017

Pennsylvania, Pittsburgh, USA

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HSCC '17 Paper Acceptance Rate 29 of 76 submissions, 38%;

Overall Acceptance Rate 153 of 373 submissions, 41%

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Cited By

Karimov TLefaucheux EOuaknine JPurser DVaronka AWhiteland MWorrell J(2022)What’s decidable about linear loops?Proceedings of the ACM on Programming Languages10.1145/34987276:POPL(1-25)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3498727
Akshay SGenest BVyas N(2018)Distribution-based objectives for Markov Decision ProcessesProceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3209108.3209185(36-45)Online publication date: 9-Jul-2018
https://dl.acm.org/doi/10.1145/3209108.3209185
Gan TChen MLi YXia BZhan N(2018)Reachability Analysis for Solvable Dynamical SystemsIEEE Transactions on Automatic Control10.1109/TAC.2017.276378563:7(2003-2018)Online publication date: Jul-2018
https://doi.org/10.1109/TAC.2017.2763785

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