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
Orthogonal Polyhedra: Representation and Computation
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Convex Optimization
Reachability Analysis of Hybrid Systems Using Support Functions
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Efficient representation and computation of reachable sets for hybrid systems
HSCC'03 Proceedings of the 6th 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
Reachability of uncertain linear systems using zonotopes
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
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In this paper we propose an approach to over-approximate the reachable set (with bounded time and number of transitions) of a hybrid system by a finite set of polytopes. The constraints of the polytope are determined by a direction choice method. For the hybrid systems whose (1) continuous dynamics are linear, (2) invariants and guards are defined by linear inequalities, and (3) variable resets are expressed by invertible affine maps, we show that the over-approximations can be computed in polynomial time, and the overestimation can be arbitrarily reduced by decreasing the discretization time step if the continuous dynamics are all deterministic. Some experimental results are also presented to show the effectiveness of our approach.