Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Reachability Analysis Using Polygonal Projections
HSCC '99 Proceedings of the Second 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
Hybridization methods for the analysis of nonlinear systems
Acta Informatica - Hybrid Systems
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
Reachability analysis of nonlinear systems using conservative approximation
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Approximate reachability computation for polynomial systems
HSCC'06 Proceedings of the 9th 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 analysis of multi-affine systems
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
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This paper is concerned with the reachability computation for non-linear systems using hybridization. The main idea of hybridization is to approximate a non-linear vector field by a piecewise-affine one. The piecewise-affine vector field is defined by building around the set of current states of the system a simplicial domain and using linear interpolation over its vertices. To achieve a good time-efficiency and accuracy of the reachability computation on the approximate system, it is important to find a simplicial domain which, on one hand, is as large as possible and, on the other hand, guarantees a small interpolation error. In our previous work[8], we proposed a method for constructing hybridization domains based on the curvature of the dynamics and showed how the method can be applied to quadratic systems. In this paper we pursue this work further and present two main results. First, we prove an optimality property of the domain construction method for a class of quadratic systems. Second, we propose an algorithm of curvature estimation for more general non-linear systems with non-constant Hessian matrices. This estimation can then be used to determine efficient hybridization domains. We also describe some experimental results to illustrate the main ideas of the algorithm as well as its performance.