Verification for Non-polynomial Hybrid Systems Using Rational Invariants

[1]  Michel Kieffer,et al.  Construction of parametric barrier functions for dynamical systems using interval analysis , 2015, Autom..

[2]  Dong Han,et al.  A New Barrier Certificate for Safety Verification of Hybrid Systems , 2014, Comput. J..

[3]  T. Henzinger.  The theory of hybrid automata , 1996, LICS 1996.

[4]  André Platzer,et al.  A Method for Invariant Generation for Polynomial Continuous Systems , 2016, VMCAI.

[5]  Curtis Bright,et al.  Vector rational number reconstruction , 2011, ISSAC '11.

[6]  Christopher W. Brown.  QEPCAD B: a program for computing with semi-algebraic sets using CADs , 2003, SIGS.

[7]  Ian M. Mitchell,et al.  Safety verification of conflict resolution manoeuvres , 2001, IEEE Trans. Intell. Transp. Syst..

[8]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[9]  George E. Collins,et al.  Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .

[10]  Alexandre Donzé,et al.  Breach, A Toolbox for Verification and Parameter Synthesis of Hybrid Systems , 2010, CAV.

[11]  T. J. Rivlin.  The Chebyshev polynomials , 1974 .

[12]  Liang Zou,et al.  Abstraction of Elementary Hybrid Systems by Variable Transformation , 2014, FM.

[13]  Siegfried M. Rump,et al.  INTLAB - INTerval LABoratory , 1998, SCAN.

[14]  Antonis Papachristodoulou,et al.  A Decomposition Technique for Nonlinear Dynamical System Analysis , 2012, IEEE Transactions on Automatic Control.

[15]  Edmund M. Clarke,et al.  Computing differential invariants of hybrid systems as fixedpoints , 2008, Formal Methods Syst. Des..

[16]  Rafael Wisniewski,et al.  Compositional safety analysis using barrier certificates , 2012, HSCC '12.

[17]  Sumit Gulwani,et al.  Constraint-Based Approach for Analysis of Hybrid Systems , 2008, CAV.

[18]  Henny B. Sipma,et al.  Constructing invariants for hybrid systems , 2008, Formal Methods Syst. Des..

[19]  A. Trofino,et al.  LMI stability conditions for uncertain rational nonlinear systems , 2014 .

[20]  Wei Chen,et al.  dReach: δ-Reachability Analysis for Hybrid Systems , 2015, TACAS.

[21]  S. Chevillard,et al.  A Certified Infinite Norm for the Implementation of Elementary Functions , 2007 .

[22]  A. Papachristodoulou,et al.  Analysis of Non-polynomial Systems using the Sum of Squares Decomposition , 2005 .

[23]  Xiaodong Liu,et al.  Requirements model driven adaption and evolution of Internetware , 2014, Science China Information Sciences.

[24]  E. Voit,et al.  Recasting nonlinear differential equations as S-systems: a canonical nonlinear form , 1987 .

[25]  Xin Chen,et al.  Flow*: An Analyzer for Non-linear Hybrid Systems , 2013, CAV.

[26]  Michel Kieffer,et al.  Computation of parametric barrier functions for dynamical systems using interval analysis , 2014, 53rd IEEE Conference on Decision and Control.

[27]  Marie-Françoise Roy,et al.  Real algebraic geometry , 1992 .

[28]  Wan Fokkink,et al.  Maximal Synthesis for Hennessy-Milner Logic , 2015, ACM Trans. Embed. Comput. Syst..

[29]  P. Parrilo.  Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .

[30]  Zhenbing Zeng,et al.  Exact safety verification of hybrid systems using sums-of-squares representation , 2011, Science China Information Sciences.

[31]  George J. Pappas,et al.  A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates , 2007, IEEE Transactions on Automatic Control.

[32]  Kai Hormann,et al.  Barycentric rational interpolation with no poles and high rates of approximation , 2007, Numerische Mathematik.

[33]  Sriram Sankaranarayanan,et al.  S-TaLiRo: A Tool for Temporal Logic Falsification for Hybrid Systems , 2011, TACAS.

[34]  Ashish Tiwari,et al.  Generating Polynomial Invariants for Hybrid Systems , 2005, HSCC.

[35]  Keith O. Geddes.  Block Structure in the Chebyshev–Padé Table , 1981 .

[36]  Siegfried M. Rump.  Verification methods: Rigorous results using floating-point arithmetic , 2010, Acta Numerica.

[37]  Stephen Prajna.  Barrier certificates for nonlinear model validation , 2006, Autom..

[38]  Hui Kong,et al.  Exponential-Condition-Based Barrier Certificate Generation for Safety Verification of Hybrid Systems , 2013, CAV.

[39]  Graziano Chesi,et al.  Estimating the domain of attraction for non-polynomial systems via LMI optimizations , 2009, Autom..

[40]  Barbara König,et al.  Tools and Algorithms for the Construction and Analysis of Systems , 2012, Lecture Notes in Computer Science.

[41]  Sriram Sankaranarayanan,et al.  Automatic invariant generation for hybrid systems using ideal fixed points , 2010, HSCC '10.

[42]  Tarik Taleb,et al.  Toward an Effective Risk-Conscious and Collaborative Vehicular Collision Avoidance System , 2010, IEEE Transactions on Vehicular Technology.

[43]  Ronald A. DeVore,et al.  Multivariate rational approximation , 1986 .

[44]  Naijun Zhan,et al.  Computing semi-algebraic invariants for polynomial dynamical systems , 2011, 2011 Proceedings of the Ninth ACM International Conference on Embedded Software (EMSOFT).

[45]  David Elliott,et al.  Error of truncated Chebyshev series and other near minimax polynomial approximations , 1987 .

[46]  Liyun Dai,et al.  Barrier certificates revisited , 2013, J. Symb. Comput..

[47]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[48]  Stefan Ratschan,et al.  Safety verification of hybrid systems by constraint propagation-based abstraction refinement , 2007, TECS.

[49]  Min Wu,et al.  Exact Safety Verification of Hybrid Systems Based on Bilinear SOS Representation , 2012, ACM Trans. Embed. Comput. Syst..

[50]  Jean B. Lasserre,et al.  Moments and sums of squares for polynomial optimization and related problems , 2009, J. Glob. Optim..

[51]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[52]  E. Saff.  On the degree of best rational approximation to the exponential function , 1973 .

[53]  Ashish Tiwari,et al.  Verification and synthesis using real quantifier elimination , 2011, ISSAC '11.

[54]  R. Baker Kearfott,et al.  Introduction to Interval Analysis , 2009 .

[55]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .