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Title: Numerical Scheme for Viability Computation Using Randomized Technique with Linear Programming

Abstract

We deal with the problem of computing viability sets for nonlinear continuous or hybrid systems. Our main objective is to beat the curse of dimensionality, that is, we want to avoid the exponential growth of required computational resource with respect to the dimension of the system. We propose a randomized approach for viability computation: we avoid griding the state-space, use random extraction of points instead, and the computation of viable set test is formulated as a classical feasibility problem. This algorithm was implemented successfully to linear and nonlinear examples. We provide comparison of our results with results of other method.

Authors:
 [1]
  1. ETH-Zurich, Automatic Control Laboratory, 8092 Zurich (Switzerland)
Publication Date:
OSTI Identifier:
21143563
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 1019; Journal Issue: 1; Conference: CISA 08: 1. Mediterranean conference on intelligent systems and automation, Annaba (Algeria), 30 Jun - 2 Jul 2008; Other Information: DOI: 10.1063/1.2953001; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; COMPARATIVE EVALUATIONS; FUZZY LOGIC; HYBRID SYSTEMS; LINEAR PROGRAMMING; NEURAL NETWORKS; NONLINEAR PROBLEMS; RANDOMNESS; SPACE

Citation Formats

Djeridane, Badis. Numerical Scheme for Viability Computation Using Randomized Technique with Linear Programming. United States: N. p., 2008. Web. doi:10.1063/1.2953001.
Djeridane, Badis. Numerical Scheme for Viability Computation Using Randomized Technique with Linear Programming. United States. https://doi.org/10.1063/1.2953001
Djeridane, Badis. 2008. "Numerical Scheme for Viability Computation Using Randomized Technique with Linear Programming". United States. https://doi.org/10.1063/1.2953001.
@article{osti_21143563,
title = {Numerical Scheme for Viability Computation Using Randomized Technique with Linear Programming},
author = {Djeridane, Badis},
abstractNote = {We deal with the problem of computing viability sets for nonlinear continuous or hybrid systems. Our main objective is to beat the curse of dimensionality, that is, we want to avoid the exponential growth of required computational resource with respect to the dimension of the system. We propose a randomized approach for viability computation: we avoid griding the state-space, use random extraction of points instead, and the computation of viable set test is formulated as a classical feasibility problem. This algorithm was implemented successfully to linear and nonlinear examples. We provide comparison of our results with results of other method.},
doi = {10.1063/1.2953001},
url = {https://www.osti.gov/biblio/21143563}, journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1019,
place = {United States},
year = {Thu Jun 12 00:00:00 EDT 2008},
month = {Thu Jun 12 00:00:00 EDT 2008}
}