Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Reachability Analysis Using Polygonal Projections
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Predicate abstraction for reachability analysis of hybrid systems
ACM Transactions on Embedded Computing Systems (TECS)
Algorithmic analysis of polygonal hybrid systems, part I: Reachability
Theoretical Computer Science
PHAVer: algorithmic verification of hybrid systems past HyTech
International Journal on Software Tools for Technology Transfer (STTT)
Model checking of analog systems using an analog specification language
Proceedings of the conference on Design, automation and test in Europe
Electronic Circuit & System Simulation Methods (SRE)
Electronic Circuit & System Simulation Methods (SRE)
Low dimensional hybrid systems - decidable, undecidable, don't know
Information and Computation
Reachability of uncertain linear systems using zonotopes
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Compositional safety analysis using barrier certificates
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Reachability analysis of non-linear planar autonomous systems
FSEN'11 Proceedings of the 4th IPM international conference on Fundamentals of Software Engineering
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We propose a methodology for reachability analysis of nonlinear analog circuits to verify safety properties. Our iterative reachable set reduction algorithm initially considers the entire state space as reachable. Our algorithm iteratively determines which regions in the state space are unreachable and removes those unreachable regions from the over approximated reachable set. We use the State Partitioning Tree (SPT) algorithm to recursively partition the reachable set into convex polytopes. We determine the reachability of adjacent neighbor polytopes by analyzing the direction of state space trajectories at the common faces between two adjacent polytopes. We model the direction of the trajectories as a reachability decision function that we solve using a sound root counting method. We are faithful to the nonlinearities of the system. We demonstrate the memory efficiency of our algorithm through computation of the reachable set of Van der Pol oscillation circuit.