Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Reachability Analysis Using Polygonal Projections
HSCC '99 Proceedings of the Second 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
Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems
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
Verifying Safety Properties of Differential Equations
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Reachability analysis of nonlinear systems using conservative approximation
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
PHAVer: algorithmic verification of hybrid systems past hytech
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
Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Reachability Analysis of Hybrid Systems Using Support Functions
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Computing Reachable States for Nonlinear Biological Models
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Accurate hybridization of nonlinear systems
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Comparing forward and backward reachability as tools for safety analysis
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Reachability algorithm for biological piecewise-affine hybrid systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Using redundant constraints for refinement
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
Computing reachable states for nonlinear biological models
Theoretical Computer Science
Reachable set computation for uncertain time-varying linear systems
Proceedings of the 14th international conference on Hybrid systems: computation and control
Hybridization domain construction using curvature estimation
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
Formal verification of hybrid systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Discretizing affine hybrid automata with uncertainty
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Avoiding geometric intersection operations in reachability analysis of hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Computing the viability kernel using maximal reachable sets
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Proceedings of the 49th Annual Design Automation Conference
Verification of Safety and Liveness Properties of Metric Transition Systems
ACM Transactions on Embedded Computing Systems (TECS) - Special Section on CAPA'09, Special Section on WHS'09, and Special Section VCPSS' 09
Reachability analysis of polynomial systems using linear programming relaxations
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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
| Hi-index | 0.02 |
This work is concerned with the problem of computing the set of reachable states for linear time-invariant systems with bounded inputs. Our main contribution is a novel algorithm which improves significantly the computational complexity of reachability analysis. Algorithms to compute over and under-approximations of the reachable sets are proposed as well. These algorithms are not subject to the wrapping effect and therefore our approximations are tight. We show that these approximations are useful in the context of hybrid systems verification and control synthesis. The performance of a prototype implementation of the algorithm confirms its qualities and gives hope for scaling up verification technology for continuous and hybrid systems.