Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
A note on a method for generating points uniformly on n-dimensional spheres
Communications of the ACM
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Optimization over Zonotopes and Training Support Vector Machines
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations
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
Journal of Computer and System Sciences
Efficient representation and computation of reachable sets for hybrid systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
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
Generating and Analyzing Symbolic Traces of Simulink/Stateflow Models
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
Proving the Correctness of the Implementation of a Control-Command Algorithm
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Reachable set computation for uncertain time-varying linear systems
Proceedings of the 14th international conference on Hybrid systems: computation and control
A dynamic algorithm for approximate flow computations
Proceedings of the 14th international conference on Hybrid systems: computation and control
A logical product approach to zonotope intersection
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Finite abstractions for hybrid systems with stable continuous dynamics
Discrete Event Dynamic Systems
Avoiding geometric intersection operations in reachability analysis of hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
An operational semantics for Simulink's simulation engine
Proceedings of the 13th ACM SIGPLAN/SIGBED International Conference on Languages, Compilers, Tools and Theory for Embedded Systems
Limited-information control of hybrid systems via reachable set propagation
Proceedings of the 16th international conference on Hybrid systems: computation and control
Spatio-temporal hybrid automata for safe cyber-physical systems: a medical case study
Proceedings of the ACM/IEEE 4th International Conference on Cyber-Physical Systems
Finite data-rate feedback stabilization of switched and hybrid linear systems
Automatica (Journal of IFAC)
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In this paper, we are concerned with the problem of computing the reachable sets of hybrid systems with (possibly high dimensional) linear continuous dynamics and guards defined by switching hyperplanes. For the reachability analysis of the continuous dynamics, we use an efficient approximation algorithm based on zonotopes. In order to use this technique for the analysis of hybrid systems, we must also deal with the discrete transitions in a satisfactory (i.e. scalable and accurate) way. For that purpose, we need to approximate the intersection of the continuous reachable sets with the guards enabling the discrete transitions. The main contribution of this paper is a novel algorithm for computing efficiently a tight over-approximation of the intersection of (possibly high-order) zonotopes with a hyperplane. We show the accuracy and the scalability of our approach by considering two examples of reachability analysis of hybrid systems.