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Forward Reachability Computation for Autonomous Max-Plus-Linear Systems [chapter]

Dieky Adzkiya, Bart De Schutter, Alessandro Abate
<span title="">2014</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;
This work discusses the computation of forward reachability for autonomous (that is, deterministic) Max-Plus-Linear (MPL) systems, a class of continuous-space discrete-event models that are relevant for  ...  We further display the computational performance of the approach by two concluding numerical benchmarks: the technique comfortably handles reachability computations over twenty-dimensional MPL models (  ...  Conclusions and Future Work This work has discussed the computation of forward reachability analysis of Max-Plus-Linear models by fast manipulations of DBM through PWA dynamics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-54862-8_17">doi:10.1007/978-3-642-54862-8_17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l3ayvwg55rd6pbeifltu3uakma">fatcat:l3ayvwg55rd6pbeifltu3uakma</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190502084127/https://link.springer.com/content/pdf/10.1007%2F978-3-642-54862-8_17.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/53/b6/53b6e124f400d882093f0451665a87eb4376f296.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-54862-8_17"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Safety Verification of Uncertain Max-Plus-Linear Systems

Aditya Putra Pratama, Subchan Subchan, Dieky Adzkiya
<span title="2018-08-17">2018</span> <i title="Lembaga Penelitian dan Pengabdian kepada Masyarakat ITS"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/k3xzsd27yngzljinnfh7cmzxhq" style="color: black;">International Journal of Computing Science and Applied Mathematics</a> </i> &nbsp;
In this work, we discussed the verification of autonomous uncertain Max-Plus-Linear (uncertain MPL) systems with respect to safety property by using the reachability analysis approach.  ...  If the unsafe set is reachable, then the system is not safe. Otherwise, the system is safe. Our approach uses the piecewise affine representation of MPL systems to compute the reachable sets exactly.  ...  Safety Verification of Uncertain Max-Plus-Linear Systems Aditya Putra Pratama, Subchan and Dieky Adzkiya Abstract-In this work, we discussed the verification of autonomous uncertain Max-Plus-Linear (uncertain  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.12962/j24775401.v4i2.3454">doi:10.12962/j24775401.v4i2.3454</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5hw2xhpuszfgrcy5574szqiz4q">fatcat:5hw2xhpuszfgrcy5574szqiz4q</a> </span>
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Backward Reachability of Autonomous Max-Plus-Linear Systems

Dieky Adzkiya, Bart De Schutter, Alessandro Abate
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p3wtlm3j2fedxitkuu4bs3scau" style="color: black;">IFAC Proceedings Volumes</a> </i> &nbsp;
This work discusses the backward reachability of autonomous Max-Plus-Linear (MPL) systems, a class of continuous-space discrete-event models that are relevant for applications dealing with synchronization  ...  Furthermore, we illustrate the application of the backward reachability computations over safety and transient analysis of MPL systems.  ...  MODELS AND PRELIMINARIES Max-Plus-Linear Systems Define R ε , ε, and e respectively as R ∪ {ε}, −∞, and 0.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3182/20140514-3-fr-4046.00056">doi:10.3182/20140514-3-fr-4046.00056</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/elswqeh2pfh5fag4nu4utl2n7m">fatcat:elswqeh2pfh5fag4nu4utl2n7m</a> </span>
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VeriSiMPL: Verification via biSimulations of MPL Models [chapter]

Dieky Adzkiya, Alessandro Abate
<span title="">2013</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;
VeriSiMPL ("very simple") is a software tool to obtain finite abstractions of Max-Plus-Linear (MPL) models.  ...  The toolbox is available at http://sourceforge.net/projects/verisimpl/ Motivations and Goals Max-Plus-Linear (MPL) models are discrete-event systems [1],[5] with continuous variables that express the timing  ...  Such a transition can be determined by forward-reachability computation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-40196-1_22">doi:10.1007/978-3-642-40196-1_22</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pvwliboejjfybjzbocbfgtiebm">fatcat:pvwliboejjfybjzbocbfgtiebm</a> </span>
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Finite abstractions of nonautonomous Max-Plus-Linear systems

Dieky Adzkiya, Bart De Schutter, Alessandro Abate
<span title="">2013</span> <i title="IEEE"> 2013 American Control Conference </i> &nbsp;
This work puts forward a technique to generate finite abstractions of nonautonomous Max-Plus-Linear (MPL) models, a known class of discrete-event systems characterizing the timing related to event counters  ...  The computational performance of the abstraction procedure is tested on a numerical benchmark.  ...  Computationally, this characterization is performed by forward-reachability analysis over a piece-wise affine (PWA, i.e. linear plus constant, over regions of the state space) representation of the MPL  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/acc.2013.6580515">doi:10.1109/acc.2013.6580515</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n4y2wfagmbbllflixtpllhybmy">fatcat:n4y2wfagmbbllflixtpllhybmy</a> </span>
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Finite Abstractions of Max-Plus-Linear Systems

Dieky Adzkiya, Bart De Schutter, Alessandro Abate
<span title="">2013</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tiaci7xy45hczhz755zlpu5h7q" style="color: black;">IEEE Transactions on Automatic Control</a> </i> &nbsp;
This work puts forward a novel technique to generate finite abstractions of autonomous and nonautonomous Max-Plus-Linear (MPL) models, a class of discrete-event systems used to characterize the dynamics  ...  of the timing related to successive events that synchronize autonomously.  ...  Max-Plus-Linear Systems Define R ε , ε and e respectively as R ∪ {ε}, −∞ and 0.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tac.2013.2273299">doi:10.1109/tac.2013.2273299</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p6y3b3x6gfa6biqjkoiveouope">fatcat:p6y3b3x6gfa6biqjkoiveouope</a> </span>
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Abstraction and verification of autonomous Max-Plus-Linear systems

D. Adzkiya, B. De Schutter, A. Abate
<span title="">2012</span> <i title="IEEE"> 2012 American Control Conference (ACC) </i> &nbsp;
This work investigates the use of finite abstractions for the verification of autonomous Max-Plus-Linear (MPL) models.  ...  The computational performance of the abstraction procedure is tested on a benchmark.  ...  Max-Plus-Linear Systems Define R ǫ , ǫ and e respectively as R ∪ {ǫ}, −∞ and 0. A vector with each component equal to 0 (or −∞) is also denoted by e (resp., ǫ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/acc.2012.6314945">doi:10.1109/acc.2012.6314945</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bpd26j26kbebvosmqnvyl373bi">fatcat:bpd26j26kbebvosmqnvyl373bi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809155637/http://csl.nagaokaut.ac.jp/~hirata/guest/uchida/acc12wea20/0758.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/c6/3f/c63f05013737bfdf6d21b970be039d942f5acd65.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/acc.2012.6314945"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Tropical Abstractions of Max-Plus Linear Systems [chapter]

Muhammad Syifa'ul Mufid, Dieky Adzkiya, Alessandro Abate
<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;
This paper describes the development of finite abstractions of Max-Plus-Linear (MPL) systems using tropical operations.  ...  The idea of tropical abstraction is inspired by the fact that an MPL system is a discrete-event model updating its state with operations in the tropical algebra.  ...  Acknowledgements The authors would like to acknowledge the use of the Advanced Research Computing (ARC) facility at the University of Oxford in carrying out the computational benchmark of this work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-00151-3_16">doi:10.1007/978-3-030-00151-3_16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/44eto524sbf4fajpcyvwof2pda">fatcat:44eto524sbf4fajpcyvwof2pda</a> </span>
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A non-linear set-membership approach for the control of Discrete Event Systems

M. Lhommeau, L. Jaulin, L. Hardouin
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p3wtlm3j2fedxitkuu4bs3scau" style="color: black;">IFAC Proceedings Volumes</a> </i> &nbsp;
Several authors have developed methods, in max-plus algebra, to compute control for max-plus systems.  ...  In this paper, we consider min-max-plus systems which are extensions of max-plus systems and non-linear even in the max-plus algebra view.  ...  and can solve larger problems (for example, min-max-plus systems which are non-linear in (max-plus,min-plus algebra).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3182/20121003-3-mx-4033.00015">doi:10.3182/20121003-3-mx-4033.00015</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f5qo6iipnfhwhmlczlb73tixzu">fatcat:f5qo6iipnfhwhmlczlb73tixzu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20140829215752/http://hal.inria.fr/docs/00/74/60/53/PDF/paper_lhommeau_wodes2012.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/21/78/21782368acccb298813dc0ec7c0950f4355a1a18.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3182/20121003-3-mx-4033.00015"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Technical Report: Safe, Aggressive Quadrotor Flight via Reachability-based Trajectory Design [article]

Shreyas Kousik, Patrick Holmes, Ramanarayan Vasudevan
<span title="2019-06-18">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Quadrotors can provide services such as infrastructure inspection and search-and-rescue, which require operating autonomously in cluttered environments.  ...  Autonomy is typically achieved with receding-horizon planning, where a short plan is executed while a new one is computed, because sensors receive limited information at any time.  ...  A Forward Reachable Set (FRS) is computed over all desired trajectories, plus tracking error and the body of the robot.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1904.05728v2">arXiv:1904.05728v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uli3vvrokrdurfx3xn26b3tkoa">fatcat:uli3vvrokrdurfx3xn26b3tkoa</a> </span>
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Guaranteed Safe Reachability-based Trajectory Design for a High-Fidelity Model of an Autonomous Passenger Vehicle [article]

Sean Vaskov, Utkarsh Sharma, Shreyas Kousik, Matthew Johnson-Roberson, Ramanarayan Vasudevan
<span title="2019-02-06">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
RTD consists of an offline component, where a Forward Reachable Set (FRS) is computed for the vehicle tracking parameterized trajectories; and an online part, where the FRS is used to map obstacles to  ...  Trajectory planning is challenging for autonomous cars since they operate in unpredictable environments with limited sensor horizons.  ...  Methods have also been proposed to ensure recursive feasibility for MPC, meaning a solution is available at every planning iteration, for linear systems [14] and for nonlinear systems either with two  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1902.01786v2">arXiv:1902.01786v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s2xofs7esbf7vg76iiqr6n5cya">fatcat:s2xofs7esbf7vg76iiqr6n5cya</a> </span>
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Max-Plus Algebra and System Theory: Where We Are and Where to Go Now 1

Guy Cohen, Stéphane Gaubert, Jean-Pierre Quadrat
<span title="">1998</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p3wtlm3j2fedxitkuu4bs3scau" style="color: black;">IFAC Proceedings Volumes</a> </i> &nbsp;
More than sixteen years after the beginning of a linear theory for certain discrete event systems in which max-plus algebra and similar algebraic tools play a central role, this paper attempts to summarize  ...  A preliminary discussion of geometric aspects in the max-plus algebra and their use for system theory is proposed in the last part of the paper.  ...  INTRODUCTION For what later became the Max-Plus working group at INRIA, the story about discrete event systems (DES) and max-plus algebra began in August 1981, that is more than sixteen and a half years  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1474-6670(17)42017-9">doi:10.1016/s1474-6670(17)42017-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/danaoffmpfdsla2vkf7jjxsmp4">fatcat:danaoffmpfdsla2vkf7jjxsmp4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922033606/https://www.rocq.inria.fr/metalau/quadrat/Systeme-Nantes.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/96/b9/96b9d19561134578fb48636c1b729083e8736441.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1474-6670(17)42017-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Max-plus algebra and system theory: Where we are and where to go now

Guy Cohen, Stéphane Gaubert, Jean-Pierre Quadrat
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7q5x2aosp5a55jied5vd5jba6m" style="color: black;">Annual Reviews in Control</a> </i> &nbsp;
More than sixteen years after the beginning of a linear theory for certain discrete event systems in which max-plus algebra and similar algebraic tools play a central role, this paper attempts to summarize  ...  A preliminary discussion of geometric aspects in the max-plus algebra and their use for system theory is proposed in the last part of the paper.  ...  INTRODUCTION For what later became the Max-Plus working group at INRIA, the story about discrete event systems (DES) and max-plus algebra began in August 1981, that is more than sixteen and a half years  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1367-5788(99)90091-3">doi:10.1016/s1367-5788(99)90091-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4n63egv2djgmhkmhcogm7uydya">fatcat:4n63egv2djgmhkmhcogm7uydya</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922033606/https://www.rocq.inria.fr/metalau/quadrat/Systeme-Nantes.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/96/b9/96b9d19561134578fb48636c1b729083e8736441.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1367-5788(99)90091-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Max-plus algebra and system theory: where we are and where to go now

G Cohen
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7q5x2aosp5a55jied5vd5jba6m" style="color: black;">Annual Reviews in Control</a> </i> &nbsp;
More than sixteen years after the beginning of a linear theory for certain discrete event systems in which max-plus algebra and similar algebraic tools play a central role, this paper attempts to summarize  ...  A preliminary discussion of geometric aspects in the max-plus algebra and their use for system theory is proposed in the last part of the paper.  ...  INTRODUCTION For what later became the Max-Plus working group at INRIA, the story about discrete event systems (DES) and max-plus algebra began in August 1981, that is more than sixteen and a half years  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1367-5788(99)00023-1">doi:10.1016/s1367-5788(99)00023-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kiaaubkad5gmtmp2kltzzm6na4">fatcat:kiaaubkad5gmtmp2kltzzm6na4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922033606/https://www.rocq.inria.fr/metalau/quadrat/Systeme-Nantes.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/96/b9/96b9d19561134578fb48636c1b729083e8736441.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1367-5788(99)00023-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Semidefinite Outer Approximation of the Backward Reachable Set of Discrete-time Autonomous Polynomial Systems [article]

Weiqiao Han, Russ Tedrake
<span title="2018-07-26">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We approximate the backward reachable set of discrete-time autonomous polynomial systems using the recently developed occupation measure approach.  ...  Finally we solve the SDP's and obtain a sequence of outer approximations of the backward reachable set. We demonstrate our approach on three dynamical systems.  ...  They used it to approximate the forward reachable set for discrete-time polynomial systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.07725v2">arXiv:1803.07725v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iyl2tnezdfdmzdasu4hhyismuu">fatcat:iyl2tnezdfdmzdasu4hhyismuu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200826093139/https://arxiv.org/pdf/1803.07725v1.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/59/cd/59cd753b01308fef36288a08a24fa65fad134512.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.07725v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
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