Linear phase-portrait approximations for nonlinear hybrid systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Automatic analysis of hybrid systems
Automatic analysis of hybrid systems
Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
ACM Transactions on Mathematical Software (TOMS)
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Automated Analysis of an Audio Control Protocol
Proceedings of the 7th International Conference on Computer Aided Verification
Algorithmic Analysis of Nonlinear Hybrid Systems
Proceedings of the 7th International Conference on Computer Aided Verification
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Efficient solving of quantified inequality constraints over the real numbers
ACM Transactions on Computational Logic (TOCL)
Safety verification of hybrid systems by constraint propagation-based abstraction refinement
ACM Transactions on Embedded Computing Systems (TECS)
Algorithmic analysis of polygonal hybrid systems, part I: Reachability
Theoretical Computer Science
Relaxing Goodness Is Still Good
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
GSPeeDI --- A Verification Tool for Generalized Polygonal Hybrid Systems
ICTAC '09 Proceedings of the 6th International Colloquium on Theoretical Aspects of Computing
Reachability analysis of nonlinear systems using conservative approximation
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Automatic rectangular refinement of affine hybrid systems
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
A compositional algorithm for parallel model checking of polygonal hybrid systems
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
PHAVer: algorithmic verification of hybrid systems past hytech
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Reachability analysis of nonlinear analog circuits through iterative reachable set reduction
Proceedings of the Conference on Design, Automation and Test in Europe
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Many complex continuous systems are modeled as non-linear autonomous systems, i.e., by a set of differential equations with one independent variable. Exact reachability, i.e., whether a given configuration can be reached by starting from an initial configuration of the system, is undecidable in general, as one needs to know the solution of the system of equations under consideration. In this paper we address the reachability problem of planar autonomous systems approximatively.We use an approximation technique which "hybridizes" the state space in the following way: the original system is partitioned into a finite set of polygonal regions where the dynamics on each region is approximated by constant differential inclusions. Besides proving soundness, completeness, and termination of our algorithm, we present an implementation, and its application into (classical) examples taken from the literature.