Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
Beyond HYTECH: Hybrid Systems Analysis Using Interval Numerical Methods
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Zonotope/Hyperplane Intersection for Hybrid Systems Reachability Analysis
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Reachability of Uncertain Nonlinear Systems Using a Nonlinear Hybridization
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Efficient representation and computation of reachable sets for hybrid systems
HSCC'03 Proceedings of the 6th 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
PHAVer: algorithmic verification of hybrid systems past hytech
HSCC'05 Proceedings of the 8th 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
Avoiding geometric intersection operations in reachability analysis of hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Reachability analysis of nonlinear systems using conservative polynomialization and non-convex sets
Proceedings of the 16th international conference on Hybrid systems: computation and control
One-shot computation of reachable sets for differential games
Proceedings of the 16th international conference on Hybrid systems: computation and control
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This paper presents a method for using set-based approximations to the Peano-Baker series to compute overapproximations of reachable sets for linear systems with uncertain, time-varying parameters and inputs. Alternative representations for sets of uncertain system matrices are considered, including matrix polytopes, matrix zonotopes, and interval matrices. For each representation, the computational efficiency and resulting approximation error for reachable set computations are evaluated analytically and empirically. As an application, reachable sets are computed for a truck with hybrid dynamics due to a gain-scheduled yaw controller. As an alternative to computing reachable sets for the hybrid model, for which switching introduces an additional overapproximation error, the gain-scheduled controller is approximated with uncertain time-varying parameters, which leads to more efficient and more accurate reachable set computations.