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Automatic Dynamic Parallelotope Bundles for Reachability Analysis of Nonlinear Systems [article]

Edward Kim, Stanley Bak, Parasara Sridhar Duggirala
2021 arXiv   pre-print
In this paper, we investigate reachable set computation for discrete nonlinear systems based on parallelotope bundles.  ...  Reachable set computation is an important technique for the verification of safety properties of dynamical systems.  ...  Introduction One of the most widely-used techniques for performing safety analysis of nonlinear dynamical systems is reachable set computation.  ... 
arXiv:2105.11796v2 fatcat:axhdbzh5cfgudnkxxb5ekw5ajm

Reachability computation for polynomial dynamical systems

Tommaso Dreossi, Thao Dang, Carla Piazza
2017 Formal methods in system design  
This paper is concerned with the problem of computing the bounded time reachable set of a polynomial discrete-time dynamical system.  ...  The proposed algorithms adopt boxes, parallelotopes, and parallelotope bundles to construct flowpipes that contain the actual reachable sets.  ...  In Section 4.2 we compare our tool Sapo with Flow * [17] , the state-ofthe-art tool for the reachability analysis on nonlinear dynamical and hybrid systems.  ... 
doi:10.1007/s10703-016-0266-3 fatcat:7j4kur6xq5eqnep3kftajzjyby

Avoiding geometric intersection operations in reachability analysis of hybrid systems

Matthias Althoff, Bruce H. Krogh
2012 Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control - HSCC '12  
The bottleneck of many reachability analysis techniques for hybrid systems is the geometrically computed intersection with guard sets.  ...  Reachability analysis is one of the promising methods for hybrid system verification, which together with all other verification techniques faces the challenge of making the analysis scale with respect  ...  Air Force Office of Scientific Research grant number FA9550-06-1-0312.  ... 
doi:10.1145/2185632.2185643 dblp:conf/hybrid/AlthoffK12 fatcat:fivmxbmqlrg53mjdgxzl2a7hae

Guaranteed State Estimation for Nonlinear Discrete-Time Systems via Indirectly Implemented Polytopic Set Computation

Jian Wan, Sanjay Sharma, Robert Sutton
2018 IEEE Transactions on Automatic Control  
This paper proposes a new set-membership technique to implement polytopic set computation for nonlinear discrete-time systems indirectly.  ...  The proposed set-membership technique is applied to solve the guaranteed state estimation problem for nonlinear discrete-time systems with a bounded description of noises and parameters.  ...  The intersection of zonotopes was called a zonotope bundle in [17] and it was used for the efficient computation of reachable sets.  ... 
doi:10.1109/tac.2018.2816262 fatcat:vabztftv6zbm5lv653s2nef52e

ARCH-COMP21 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

Luca Geretti, Julien Alexandre Dit Sandretto, Matthias Althoff, Luis Benet, Alexandre Chapoutot, Pieter Collins, Parasara Sridhar Duggirala, Marcelo Forets, Edward Kim, Uziel Linares, David P. Sanders, Christian Schilling (+1 others)
We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics.  ...  These tools are applied to solve reachability analysis problems on five benchmark problems, two of them featuring hybrid dynamics.  ...  Automatic dynamic parallelotope bundles for reachability analysis of nonlinear systems, 2021. arXiv:2105.11796. [26] Edward Kim and Parasara Sridhar Duggirala.  ... 
doi:10.29007/2jw8 fatcat:xlmbgk46qzc2vd2m4j6hcbqbke

A Link to the Math. Connections Between Number Theory and Other Mathematical Topics

Martin Kreh
Definition I.3.1 Let (M, A , µ, T) be a dynamical system over a probability space.  ...  Measure spaces and Dynamical Systems Let us recall some definitions from measure theory. For more information see [Kle08] .  ...  Appendix Due to Lemma II. 4 .12 we have B > 1 πn δ for some constant δ, i.e., |R M (n)| < 1 n log 1 For the convergence of R L (n) we note that f (x) is monotone decreasing for x ∈ [0, ξ), thus we have  ... 
doi:10.18442/805 fatcat:kl7abso7izfovm3jy7bdqw2x6a