The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
&egr;-approximation of differential inclusions
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Ellipsoidal Techniques for Reachability Analysis
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Level Set Methods for Computation in Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Hybridization methods for the analysis of nonlinear systems
Acta Informatica - Hybrid Systems
Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Reachability Analysis of Hybrid Systems Using Support Functions
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Verifying Tolerant Systems Using Polynomial Approximations
RTSS '09 Proceedings of the 2009 30th IEEE Real-Time Systems Symposium
Accurate hybridization of nonlinear systems
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Reachability for linear hybrid automata using iterative relaxation abstraction
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Verification of hybrid systems based on counterexample-guided abstraction refinement
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Counter-example guided predicate abstraction of hybrid systems
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
CAV'07 Proceedings of the 19th international conference on Computer aided verification
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
Algorithmic algebraic model checking i: challenges from systems biology
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Refining abstractions of hybrid systems using counterexample fragments
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Reachability of uncertain linear systems using zonotopes
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Flowpipe approximation and clustering in space-time
Proceedings of the 16th international conference on Hybrid systems: computation and control
Abstraction based model-checking of stability of hybrid systems
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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In this paper we consider the problem of approximating the set of states reachable within a time bound T in a linear dynamical system, to within a given error bound ε. Fixing a degree d, our algorithm divides the interval [0,T] into sub-intervals of not necessarily equal size, such that a polynomial of degree d approximates the actual flow to within an error bound of ε, and approximates the reach set within each sub-interval by the polynomial tube. Our experimental evaluation of the algorithm when the degree d is fixed to be either 1 or 2, shows that the approach is promising, as it scales to large dimensional dynamical systems, and performs better than previous approaches that divided the interval [0,T] evenly into sub-intervals.