Theoretical Computer Science
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
What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Deciding reachability for planar multi-polynomial systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
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
A Geometric Approach to Bisimulation and Verification of Hybrid Systems
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
A New Class of Decidable Hybrid Systems
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
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
On the Decidability of the Reachability Problem for Planar Differential Inclusions
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Reachability Analysis of Planar Multi-limear Systems
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
Widening the Boundary between Decidable and Undecidable Hybrid Systems
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
On the Decidability of the Reachability Problem for Planar Differential Inclusions
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Towards Computing Phase Portraits of Polygonal Differential Inclusions
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
SPeeDI - A Verification Tool for Polygonal Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Reachability in Linear Dynamical Systems
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Relaxing Goodness Is Still Good
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
Computing Omega-Limit Sets in Linear Dynamical Systems
UC '08 Proceedings of the 7th international conference on Unconventional Computing
Computation in one-dimensional piecewise maps and planar pseudo-billiard systems
UC'05 Proceedings of the 4th international conference on Unconventional Computation
Static analysis for state-space reduction of polygonal hybrid systems
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
A compositional algorithm for parallel model checking of polygonal hybrid systems
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Low dimensional hybrid systems - decidable, undecidable, don't know
Information and Computation
Refining the undecidability frontier of hybrid automata
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
| Hi-index | 0.00 |
In this paper we develop an algorithm for solving the reachability problem of two-dimensional piece-wise rectangular differential inclusions. Our procedure is not based on the computation of the reach-set but rather on the computation of the limit of individual trajectories. A key idea is the use of one-dimensional affine PoincarÉ maps for which we can easily compute the fixpoints. As a first step, we show that between any two points linked by an arbitrary trajectory there always exists a trajectory without self-crossings. Thus, solving the reachability problem requires considering only those. We prove that, indeed, there are only finitely many "qualitative types" of those trajectories. The last step consists in giving a decision procedure for each of them. These procedures are essentially based on the analysis of the limits of extreme trajectories. We illustrate our algorithm on a simple model of a swimmer spinning around a whirlpool.