Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Functional composition algorithms via blossoming
ACM Transactions on Graphics (TOG)
Change of basis algorithms for surfaces in CAGD
Computer Aided Geometric Design
Curves and surfaces in geometric modeling: theory and algorithms
Curves and surfaces in geometric modeling: theory and algorithms
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
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
Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Series of Abstractions for Hybrid Automata
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Reachability Analysis of Hybrid Systems via Predicate Abstraction
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Reachability analysis of nonlinear systems using conservative approximation
HSCC'03 Proceedings of the 6th 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
A toolbox of hamilton-jacobi solvers for analysis of nondeterministic continuous and hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Analysis for dynamic of analog circuits by using HSPN
ICC'07 Proceedings of the 11th Conference on Proceedings of the 11th WSEAS International Conference on Circuits - Volume 11
Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion
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
Robust stabilisation of polynomial systems with uncertain parameters
International Journal of Systems Science
Computing reachable states for nonlinear biological models
Theoretical Computer Science
Hybridization domain construction using curvature estimation
Proceedings of the 14th international conference on Hybrid systems: computation and control
Reachability analysis of polynomial systems using linear programming relaxations
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Hybrid control lyapunov functions for the stabilization of hybridsystems
Proceedings of the 16th international conference on Hybrid systems: computation and control
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In this paper we propose an algorithm for approximating the reachable sets of systems defined by polynomial differential equations. Such systems can be used to model a variety of physical phenomena. We first derive an integration scheme that approximates the state reachable in one time step by applying some polynomial map to the current state. In order to use this scheme to compute all the states reachable by the system starting from some initial set, we then consider the problem of computing the image of a set by a multivariate polynomial. We propose a method to do so using the Bézier control net of the polynomial map and the blossoming technique to compute this control net. We also prove that our overall method is of order 2. In addition, we have successfully applied our reachability algorithm to two models of a biological system.