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Efficient Dynamic Error Reduction for Hybrid Systems Reachability Analysis [chapter]

Stefan Schupp, Erika Ábrahám
<span title="">2018</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
To decide whether a set of states is reachable in a hybrid system, over-approximative symbolic successor computations can be used, where the symbolic representation of state sets as well as the successor  ...  computations have several parameters which determine the efficiency and the precision of the computations.  ...  Hybrid automata [3] are one of the modeling formalisms for hybrid systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-89963-3_17">doi:10.1007/978-3-319-89963-3_17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mfjnx36pgzgxlajzknckxomhzu">fatcat:mfjnx36pgzgxlajzknckxomhzu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190225235922/http://pdfs.semanticscholar.org/69b6/22b9169866695c7b8cd701873756e394ae94.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/69/b6/69b622b9169866695c7b8cd701873756e394ae94.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-89963-3_17"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Current Challenges in the Verification of Hybrid Systems [chapter]

Stefan Schupp, Erika Ábrahám, Xin Chen, Ibtissem Ben Makhlouf, Goran Frehse, Sriram Sankaranarayanan, Stefan Kowalewski
<span title="">2015</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Latest developments brought interesting theoretical results and powerful tools for the reachability analysis of hybrid systems.  ...  the verification of hybrid systems.  ...  Hybrid Systems Modelling and Reachability Analysis Hybrid systems are systems with combined discrete-continuous behaviour.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-25141-7_2">doi:10.1007/978-3-319-25141-7_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zvdce2gma5hwfnpeid64dstaki">fatcat:zvdce2gma5hwfnpeid64dstaki</a> </span>
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Recent progress in continuous and hybrid reachability analysis

Eugene Asarin, Thao Dang, Goran Frehse, Antoine Girard, Colas Le Guernic, Oded Maler
<span title="">2006</span> <i title="IEEE"> 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control </i> &nbsp;
Due to its inherent complexity, the application of reachability analysis has been limited so far to simple systems, both in the continuous and the hybrid domain.  ...  Set-based reachability analysis computes all possible states a system may attain, and in this sense provides knowledge about the system with a completeness, or coverage, that a finite number of simulation  ...  HYBRID SYSTEMS AND REACHABILITY ANALYSIS The interaction of discrete events and continuous, timedriven dynamics can be efficiently modeled by a so-called hybrid automaton [1] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cacsd-cca-isic.2006.4776877">doi:10.1109/cacsd-cca-isic.2006.4776877</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hipfmslmorgtzjm56vw3rmrpju">fatcat:hipfmslmorgtzjm56vw3rmrpju</a> </span>
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Reachability Analysis of Stochastic Hybrid Systems: A Biodiesel Production System

Derek Riley, Kasandra Riley, Xenofon Koutsoukos
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mgvedi22fvcvbf2sn6s7wpfn7y" style="color: black;">European Journal of Control</a> </i> &nbsp;
Reachability analysis of stochastic hybrid systems (SHS) is an important problem because it provides a formal framework to analyze complex systems.  ...  Analysis of a biodiesel production system is important to understand and analyze because demand for biofuels is growing, and economical, efficient production methods will result in high-quality, lower  ...  SHS extend hybrid systems by considering stochastic dynamics and providing a probabilistic framework for modeling and analysis of biochemical systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3166/ejc.16.609-623">doi:10.3166/ejc.16.609-623</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h3gcnij2enh7xht7pgum5kgezm">fatcat:h3gcnij2enh7xht7pgum5kgezm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20111004185524/http://www.vuse.vanderbilt.edu/~koutsoxd/www/Publications/SHSJ09.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ce/b8/ceb8d4baaf690d2a034473d8e55df7c6dcc2ccdb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3166/ejc.16.609-623"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Constructing verification models of nonlinear Simulink systems via syntactic hybridization

Nikolaos Kekatos, Marcelo Forets, Goran Frehse
<span title="">2017</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">2017 IEEE 56th Annual Conference on Decision and Control (CDC)</a> </i> &nbsp;
The focus is on set-based reachability analysis and on control systems that are described by hybrid dynamics and nonlinear components.  ...  A major obstacle here is that highly scalable reachability algorithms and tools exist for piecewise affine (PWA) dynamical models, but not for nonlinear ones.  ...  ACKNOWLEDGEMENT The authors would like to thank Willem Hagemann and Stefano Minopoli for valuable discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2017.8263907">doi:10.1109/cdc.2017.8263907</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/KekatosFF17.html">dblp:conf/cdc/KekatosFF17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3mjjeu6y5vdftifdm2zuw6c6mm">fatcat:3mjjeu6y5vdftifdm2zuw6c6mm</a> </span>
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Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis [chapter]

Antoine Girard, Colas Le Guernic
<span title="">2008</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
For the reachability analysis of the continuous dynamics, we use an efficient approximation algorithm based on zonotopes.  ...  We show the accuracy and the scalability of our approach by considering two examples of reachability analysis of hybrid systems.  ...  Hybrid reachability We now discuss the use of Algorithm 1 for reachability analysis of a hybrid system.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-78929-1_16">doi:10.1007/978-3-540-78929-1_16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xqapj2derfbornb23f2ddk74za">fatcat:xqapj2derfbornb23f2ddk74za</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810150526/http://www-ljk.imag.fr/membres/Antoine.Girard/Publications/hscc2008b.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8c/e4/8ce4591cbc2de5d019120ca50588cc68a0902e61.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-78929-1_16"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Time Domain Verification of Oscillator Circuit Properties

Goran Frehse, Bruce H. Krogh, Rob A. Rutenbar, Oded Maler
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
The approach is illustrated for a nonlinear tunneldiode circuit model using PHAVer, a hybrid system analysis tool that provides sound verification results based on linear hybrid automata approximations  ...  Generic monitor automata are proposed to facilitate the application of hybrid system reachability computations to characterize time domain features of oscillatory behavior, such as bounds on the signal  ...  for hybrid systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2006.02.019">doi:10.1016/j.entcs.2006.02.019</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b4qenuu62fcr7h4fh7rguagpou">fatcat:b4qenuu62fcr7h4fh7rguagpou</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810150818/https://users.ece.cmu.edu/~krogh/papers/FKRM06.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9c/11/9c113f7c3f72cc3e2fb51aa65261aa121e413a82.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2006.02.019"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

Reachable set computation for uncertain time-varying linear systems

Matthias Althoff, Colas Le Guernic, Bruce H. Krogh
<span title="">2011</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hvggws4aarca5da3cwlmumbtr4" style="color: black;">Proceedings of the 14th international conference on Hybrid systems: computation and control - HSCC &#39;11</a> </i> &nbsp;
As an application, reachable sets are computed for a truck with hybrid dynamics due to a gain-scheduled yaw controller.  ...  For each representation, the computational efficiency and resulting approximation error for reachable set computations are evaluated analytically and empirically.  ...  Reachable sets of such systems can be used as a basis for the reachability analysis of linear or even more complex systems, such as nonlinear and hybrid systems [7, 14] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1967701.1967717">doi:10.1145/1967701.1967717</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/hybrid/AlthoffGK11.html">dblp:conf/hybrid/AlthoffGK11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7pwg3jhwb5antfw6t3hbjsculm">fatcat:7pwg3jhwb5antfw6t3hbjsculm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719211017/http://mediatum.ub.tum.de/doc/1287217/document.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d3/e1/d3e1561df57b73f44be53e8a8d5bd49ad4dd25e0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1967701.1967717"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Accurate hybridization of nonlinear systems

Thao Dang, Oded Maler, Romain Testylier
<span title="">2010</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hvggws4aarca5da3cwlmumbtr4" style="color: black;">Proceedings of the 13th ACM international conference on Hybrid systems: computation and control - HSCC &#39;10</a> </i> &nbsp;
This paper is concerned with reachable set computation for non-linear systems using hybridization.  ...  In this paper we study the relationship between the region geometry and reachable set accuracy and propose a method for constructing hybridization regions using tighter interpolation error bounds.  ...  Linear dynamical systems admit nice properties that facilitate their analysis by various approaches.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1755952.1755956">doi:10.1145/1755952.1755956</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/hybrid/DangMT10.html">dblp:conf/hybrid/DangMT10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/od5yubj5vjglhef6qfznktxn4i">fatcat:od5yubj5vjglhef6qfznktxn4i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706093749/http://www-verimag.imag.fr/~maler/Papers/new-hyb.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f6/be/f6bec98a17fafddb681270187f001df791e51080.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1755952.1755956"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Reachability analysis of nonlinear systems using conservative polynomialization and non-convex sets

Matthias Althoff
<span title="">2013</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hvggws4aarca5da3cwlmumbtr4" style="color: black;">Proceedings of the 16th international conference on Hybrid systems: computation and control - HSCC &#39;13</a> </i> &nbsp;
A new technique for computing the reachable set of hybrid systems with nonlinear continuous dynamics is presented.  ...  Previous work showed that abstracting the nonlinear continuous dynamics to linear differential inclusions results in a scalable approach for reachability analysis.  ...  Acknowledgment The author likes to thank Xin Chen for support with the tool flow* and discussions on Taylor models.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2461328.2461358">doi:10.1145/2461328.2461358</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/hybrid/Althoff13.html">dblp:conf/hybrid/Althoff13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gfyv7rynj5ceraewzx6eqo2lju">fatcat:gfyv7rynj5ceraewzx6eqo2lju</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150408110123/http://www6.in.tum.de/Main/Publications/Althoff2013a.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/82/fe/82fe52ff73ccbd4476910da6d8389e1949b0c2ef.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2461328.2461358"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Symbolic-Numeric Methods for Problem Solving in CPS (Dagstuhl Seminar 16491)

Sergiy Bogomolov, Martin Fränzle, Kyoko Makino, Nacim Ramdani, Marc Herbstritt
<span title="2017-04-12">2017</span> <i title="Schloss Dagstuhl Leibniz-Zentrum für Informatik GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/u2phfyhrhje7xnnubtp3vfklcu" style="color: black;">Dagstuhl Reports</a> </i> &nbsp;
the following research areas relevant to problem solving in cyber-physical domains: verification of numerical reactive systems such as embedded floating-point programs and hybrid systems, including novel  ...  means of error-propagation analysis; numerical and/or symbolic methods such as verified integrations, interval methods and arithmetic constraint solving; reactive and in-advance planning and optimization  ...  A Com- prehensive Method for Reachability Analysis of Uncertain Nonlinear Hybrid Systems. IEEE Trans. Automat. Contr. 61(9): 2341-2356 (2016).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.6.12.1">doi:10.4230/dagrep.6.12.1</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/journals/dagstuhl-reports/BogomolovFMR16.html">dblp:journals/dagstuhl-reports/BogomolovFMR16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sydj4slvefa7boehai7gpnfupm">fatcat:sydj4slvefa7boehai7gpnfupm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220123035621/https://drops.dagstuhl.de/opus/volltexte/2017/7108/pdf/dagrep_v006_i012_p001_s16491.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c4/4e/c44e893fc9e6d5e542c7084b305cbec27323b9ab.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.6.12.1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Reachability analysis of nonlinear systems with uncertain parameters using conservative linearization

Matthias Althoff, Olaf Stursberg, Martin Buss
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">2008 47th IEEE Conference on Decision and Control</a> </i> &nbsp;
A new technique for computing the reachable set of hybrid systems with nonlinear continuous dynamics is presented.  ...  Previous work showed that abstracting the nonlinear continuous dynamics to linear differential inclusions results in a scalable approach for reachability analysis.  ...  Acknowledgment The author likes to thank Xin Chen for support with the tool flow* and discussions on Taylor models.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2008.4738704">doi:10.1109/cdc.2008.4738704</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/AlthoffSB08.html">dblp:conf/cdc/AlthoffSB08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2w7bzelqwzbtjbq5qvqiylkkl4">fatcat:2w7bzelqwzbtjbq5qvqiylkkl4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150408110123/http://www6.in.tum.de/Main/Publications/Althoff2013a.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/82/fe/82fe52ff73ccbd4476910da6d8389e1949b0c2ef.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2008.4738704"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

JuliaReach

Sergiy Bogomolov, Marcelo Forets, Goran Frehse, Kostiantyn Potomkin, Christian Schilling
<span title="">2019</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hvggws4aarca5da3cwlmumbtr4" style="color: black;">Proceedings of the 22nd ACM International Conference on Hybrid Systems Computation and Control - HSCC &#39;19</a> </i> &nbsp;
We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems.  ...  JuliaReach consists of two main packages: Reachability, containing implementations of reachability algorithms for continuous and hybrid systems, and LazySets, a standalone library that implements state-of-the-art  ...  ACKNOWLEDGMENTS This work was partially supported by the Air Force Office of Scientific Research under award number FA2386-17-1-4065, by the ARC project DP140104219 (Robust AI Planning for Hybrid Systems  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/3302504.3311804">doi:10.1145/3302504.3311804</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/hybrid/BogomolovFFPS19.html">dblp:conf/hybrid/BogomolovFFPS19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iutewqbt5jhxvb6fl7etwdvseq">fatcat:iutewqbt5jhxvb6fl7etwdvseq</a> </span>
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Complexity reduction through a Schur-based decomposition for reachability analysis of linear time-invariant systems

Shahab Kaynama, Meeko Oishi
<span title="">2011</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r467vnh32bfzre7lj4uj5cyv4a" style="color: black;">International Journal of Control</a> </i> &nbsp;
We present a method for complexity reduction in reachability analysis and controller synthesis via a Schur-based decomposition for LTI systems.  ...  Reachable sets, computed for each subsystem, are back-projected and intersected to yield an overapproximation of the actual reachable set.  ...  INTRODUCTION Reachability analysis is key for verification and controller synthesis of continuous and hybrid dynamical systems, yet a major obstacle in employing reachability analysis is the "curse of  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00207179.2010.543703">doi:10.1080/00207179.2010.543703</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mmze3joyjrecvpsdgzmpgfts3i">fatcat:mmze3joyjrecvpsdgzmpgfts3i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190217160646/http://pdfs.semanticscholar.org/0602/328c8bc1c0e6997367fdb7880df44ac95fe2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/06/02/0602328c8bc1c0e6997367fdb7880df44ac95fe2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00207179.2010.543703"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

Verifying analog oscillator circuits using forward/backward abstraction refinement

G. Frehse, B.H. Krogh, R.A. Rutenbar
<span title="">2006</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qjrrvry5ubgdlarkymvlxuip6m" style="color: black;">Proceedings of the Design Automation &amp; Test in Europe Conference</a> </i> &nbsp;
Properties of analog circuits can be verified formally by partitioning the continuous state space and applying hybrid system verification techniques to the resulting abstraction.  ...  The technique can yield dramatic memory and runtime reductions.  ...  Our aim is to develop such tools using recently developed methods to perform model checking for hybrid dynamic systems, that is, systems characterized by both continuous and discrete state variables.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/date.2006.244113">doi:10.1109/date.2006.244113</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/date/FrehseKR06.html">dblp:conf/date/FrehseKR06</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6i3zu3a53zh4fa7kt2cairz6py">fatcat:6i3zu3a53zh4fa7kt2cairz6py</a> </span>
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