TY - GEN
T1 - Reachable set computation for uncertain time-varying linear systems
AU - Althoff, Matthias
AU - Le Guernic, Colas
AU - Krogh, Bruce H.
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Linear systems
KW - Peano-Baker series
KW - Reachability analysis
KW - Safety
KW - Uncertain parameters
UR - https://www.scopus.com/pages/publications/79955988358
U2 - 10.1145/1967701.1967717
DO - 10.1145/1967701.1967717
M3 - Conference contribution
AN - SCOPUS:79955988358
SN - 9781450306294
T3 - HSCC'11 - Proceedings of the 2011 ACM/SIGBED Hybrid Systems: Computation and Control
SP - 93
EP - 102
BT - HSCC'11 - Proceedings of the 2011 ACM/SIGBED Hybrid Systems
T2 - 14th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2011
Y2 - 12 April 2011 through 14 April 2011
ER -