How good are convex hull algorithms?
Computational Geometry: Theory and Applications
HYTECH: The Cornell HYbrid TECHnology Tool
Hybrid Systems II
A New Class of Decidable Hybrid Systems
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Beyond HYTECH: Hybrid Systems Analysis Using Interval Numerical Methods
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Verification of Hybrid Systems with Linear Differential Inclusions Using Ellipsoidal Approximations
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Reachability analysis of continuous-time piecewise affine systems
Automatica (Journal of IFAC)
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
Efficient representation and computation of reachable sets for hybrid systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Reachable set computation for uncertain time-varying linear systems
Proceedings of the 14th international conference on Hybrid systems: computation and control
SpaceEx: scalable verification of hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Efficient computation of reachable sets of linear time-invariant systems with inputs
HSCC'06 Proceedings of the 9th 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
Survey Controlling mechanical systems with backlash-a survey
Automatica (Journal of IFAC)
Reachability analysis of nonlinear systems using conservative polynomialization and non-convex sets
Proceedings of the 16th international conference on Hybrid systems: computation and control
One-shot computation of reachable sets for differential games
Proceedings of the 16th international conference on Hybrid systems: computation and control
Formal verification of phase-locked loops using reachability analysis and continuization
Communications of the ACM
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Although a growing number of dynamical systems studied in various fields are hybrid in nature, the verification of properties, such as stability, safety, etc., is still a challenging problem. Reachability analysis is one of the promising methods for hybrid system verification, which together with all other verification techniques faces the challenge of making the analysis scale with respect to the number of continuous state variables. The bottleneck of many reachability analysis techniques for hybrid systems is the geometrically computed intersection with guard sets. In this work, we replace the intersection operation by a nonlinear mapping onto the guard, which is not only numerically stable, but also scalable, making it possible to verify systems which were previously out of reach. The approach can be applied to the fairly common class of hybrid systems with piecewise continuous solutions, guard sets modeled as halfspaces, and urgent semantics, i.e. discrete transitions are immediately taken when enabled by guard sets. We demonstrate the usefulness of the new approach by a mechanical system with backlash which has 101 continuous state variables.