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LazySets.jl: Scalable Symbolic-Numeric Set Computations [article]

Marcelo Forets, Christian Schilling
2021 arXiv   pre-print
In this article we showcase the basic functionality, highlighting some of the key design choices.  ...  LazySets is the core library of JuliaReach, a cutting-edge software addressing the fundamental problem of reachability analysis: computing the set of states that are reachable by a dynamical system from  ...  of neural network control policies for nonlinear systems, 2021. [24] Sigurd Skogestad and Ian Postlethwaite. Multivariable feedback control: analysis and design, volume 2.  ... 
arXiv:2110.01711v1 fatcat:g6grvdiayrg3hefym5cfl3wuaa

LazySets.jl: Scalable Symbolic-Numeric Set Computations$^*$

2021 JuliaCon Proceedings  
In this article we showcase the basic functionality, highlighting some of the key design choices.  ...  LazySets is the core library of JuliaReach, a cutting-edge software addressing the fundamental problem of reachability analysis: computing the set of states that are reachable by a dynamical system from  ...  Finally, we greatly appreciate Benoît Legat and Guillaume Dalle for their work in revising this paper.  ... 
doi:10.21105/jcon.00097 fatcat:ezb5jf5dt5gqlbbno5yh2wucru

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

Sergiy Bogomolov, Martin Fränzle, Kyoko Makino, Nacim Ramdani, Marc Herbstritt
2017 Dagstuhl Reports  
Reflecting the fundamental role numeric and mixed symbolic-numeric arguments play in the analysis, decision making, and control of cyber-physical processes, this seminar promoted crossfertilization between  ...  It naturally included the broad set of domain-specific solutions to the pertinent issues of performance impact of error propagation and control in various schemes of numeric and blended symbolic-numeric  ...  Hybrid Systems Computation Control (HSCC) and Analysis and Design of Hybrid Systems (ADHS) as well as continuous high impact on top conferences in the field of automatic verification, e.g.  ... 
doi:10.4230/dagrep.6.12.1 dblp:journals/dagstuhl-reports/BogomolovFMR16 fatcat:sydj4slvefa7boehai7gpnfupm

Algorithms for symbolic/numeric control of affine dynamical systems

Aude Rondepierre, Jean-Guillaume Dumas
2005 Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05  
In particular new efficient methods computing a block Kalman canonical exact decomposition and the optimal solutions are presented.  ...  We also propose a new numerical algorithm under-approximating the controllable domain in view of its analytical resolution in the context of singular sub-arcs.  ...  In this paper we propose a new approach via block matrix computation developed in collaboration with C.  ... 
doi:10.1145/1073884.1073923 dblp:conf/issac/RondepierreD05 fatcat:y4gcxc7565fkrid7g3tqk5nrri

Plant/controller design integration for H2 control based on symbolic-numeric hybrid optimization

Hirokazu Anai, Shinji Hara, Masaaki Kanno
2011 Communications in Information and Systems  
The framework is further equipped with a symbolic-numeric hybrid optimization approach to effectively search the optimum.  ...  However a more realistic system design (not controller design) scenario supposes some freedom in the plant that is to be controlled [9] .  ...  Symbolic-numeric Hybrid Integrated Design Approach. To this end a new framework for plant/controller design integration is proposed. The approachFig. 2.4. Proposed approach framework.  ... 
doi:10.4310/cis.2011.v11.n3.a5 fatcat:225tpdxtercjpcjp2mytxcb2gy

CFD with Hybrid Symbolic-Numeric Methodology

Jose Camberos, Larry Lambe, Richard Luczak
2004 42nd AIAA Aerospace Sciences Meeting and Exhibit   unpublished
This will introduce the reader to the hybrid methodology with the hope of inspiring new thought in utilizing symbolic manipulation to solve problems in mathematical physics from a fundamental perspective  ...  Computer power at the time, however, forced the research direction towards fully discretized, purely numerical calculations.  ...  Acknowledgments This work was sponsored by a grant from the Chief Scientist Innovative Research Fund of the Air Vehicles Directorate, U. S. Air Force Research Laboratory.  ... 
doi:10.2514/6.2004-242 fatcat:l4onyoelxvaijcwy36ism52ikq

Hybrid Symbolic-Numeric Methodology: Views and Visions

Jose Camberos, Larry Lambe, Richard Luczak
2005 43rd AIAA Aerospace Sciences Meeting and Exhibit   unpublished
We used computer aided symbolic computation in our previous papers 1, 2 to explore solutions of partial differential equations in a way that involves a synergistic application of symbolic and numeric methodologies  ...  The continued development of the hybrid methodology is presented with the hope of inspiring new thought in utilizing hybrid symbolic and numeric manipulation for solving the equations of mathematical physics  ...  In these two papers, we introduced hybrid symbolic-numeric (HSN) schemes using symbolic manipulation of expressions based on ExprLib 3-7 which is an ANSI C library designed to meet some stringent needs  ... 
doi:10.2514/6.2005-92 fatcat:htao3y6manawtm4edq7gslrbp4

LazySets.jl: Scalable Symbolic-Numeric Set Computations

Marcelo Forets, Christian Schilling
2021
In this article we showcase the basic functionality, highlighting some of the key design choices.  ...  LazySets is the core library of JuliaReach, a cutting-edge software addressing the fundamental problem of reachability analysis: computing the set of states that are reachable by a dynamical system from  ...  Finally, we greatly appreciate Benoît Legat and Guillaume Dalle for their work in revising this paper.  ... 
doi:10.48550/arxiv.2110.01711 fatcat:ndpzboxfqzh4poefjfruieijl4

Towards multi-domain knowledge transfer in engineering analyses and simulations based on virtual prototypes

Zoltán Rusák, Imre Horváth, Ferruccio Mandorli
2013 Engineering with Computers  
, in addition to presenting results of the efforts towards enhancing mono-disciplinary analysis and simulation approaches.  ...  ., design of computer experiments), (ii) introduction of novel technologies to enable simulation of complex physical phenomena (e.g., multiple contact in ropes), (iii) development of multi-physics solvers  ...  Using three levels of representation (i.e. symbolic, numeric and visual), the software is able to guide the user through a very simple workflow and enables them to design worm gear mechanisms and to generate  ... 
doi:10.1007/s00366-013-0322-1 fatcat:5cugdticmze4thlwcvi67ybmey

2019 Index IEEE Transactions on Cloud Computing Vol. 7

2020 IEEE Transactions on Cloud Computing  
-Dec. 2019 1082-1094 SNC: A Cloud Service Platform for Symbolic-Numeric Computation Using Just-In-Time Compilation.  ...  ., +, TCC April -June 2019 553-567 SNC: A Cloud Service Platform for Symbolic-Numeric Computation Using Just-In-Time Compilation.  ... 
doi:10.1109/tcc.2020.2969066 fatcat:uxhqc6ryenen7brk6qnejnciaa

University of Western Ontario

1979 Neurosurgery  
We expect also to have $50,000 in funding per year available to support a new initiative from the RCMP.  ...  This is a major award for university-industry collaboration. Robert Corless has been awarded the "Distinguished University Professor" title in 2006 at the University of Western Ontario.  ...  (x) In "Hybrid Symbolic-Numeric Integration in Multiple Dimensions via Tensor-Product Series" by Carvajal, Chapman and Geddes, a new hybrid symbolic-numeric method for the fast and accurate evaluation  ... 
doi:10.1227/00006123-197907010-00123 fatcat:u7zhv6kf4fcktaqbxlgw6kliwa

Preface

Dario Andrea Bini, Victor Y. Pan, Jan Verschelde
2008 Theoretical Computer Science  
Preface Symbolic-numerical computations (hereafter abbreviated as SNC) make up an important area of rapidly growing popularity.  ...  The basic idea is to combine towards a common goal the two rich but distinct bodies of techniques developed in the two fields of symbolic and numerical computing.  ...  Further applications include fundamental algebraic-geometric computations. Analysis and experiments confirm the power of this approach.  ... 
doi:10.1016/j.tcs.2008.09.001 fatcat:uwwutxg5svdkholg7mtcu2pvzy

Synthesizing Switching Controllers for Hybrid Systems by Generating Invariants [chapter]

Hengjun Zhao, Naijun Zhan, Deepak Kapur
2013 Lecture Notes in Computer Science  
We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials.  ...  To avoid too much human interaction in choosing templates as well as the high computational complexity caused by QE, we further investigate applications of the SOS (sum-ofsquares) relaxation approach and  ...  In [20, 48] , the authors proposed a hybrid symbolic-numeric approach to compute exact inequality invariants of hybrid systems, by first solving (bilinear) SOS programming numerically and then applying  ... 
doi:10.1007/978-3-642-39698-4_22 fatcat:na6ge7pjandallod5rdqksmyd4

Diagnosis of Hybrid Systems Using Hybrid Particle Petri Nets: Theory and Application on a Planetary Rover [chapter]

Quentin Gaudel, Elodie Chanthery, Pauline Ribot, Matthew J. Daigle
2018 Fault Diagnosis of Hybrid Dynamic and Complex Systems  
A hybrid model of the K11 is proposed and experimental results show that the approach is robust to real system data and constraints.  ...  Diagnosers are generated from these hybrid automata using a new data structure in order to monitor both the behavior and degradation of such systems.  ...  respectively symbolic, numerical and degradation markings at time k.  ... 
doi:10.1007/978-3-319-74014-0_9 fatcat:hspunr7c3ffc7efwon2yut5tju

Abstracts of Current Computer Literature

1970 IEEE transactions on computers  
The utility of the algorithm in the analysis of linear networks and systems with the desired expressions in symbolic and symbolic/ numerical forms is discussed.  ...  Sharing in a Computer Utility 7970 Automatic Analog/Hybrid Solution of an Optimal Control Problem 7973 Time-Sharing Task Control for a Hybrid Computer Simulation Laboratory 7976 Conversion; Converters  ... 
doi:10.1109/t-c.1970.223067 fatcat:fmxgtckr5vcivhopuosht7gszu
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