B.H.: Reachable set computation for uncertain timevarying linear systems

This paper presents a method for using set-based approxi-mations to the Peano-Baker series to compute overapproxi-mations of reachable sets for linear systems with uncertain, time-varying parameters and inputs. Alternative represen-tations for sets of uncertain system matrices are considered, including matrix polytopes, matrix zonotopes, and interval matrices. For each representation, the computational ef-ficiency 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 overap-proximation error, the gain-scheduled controller is approxi-mated with uncertain time-varying parameters, which leads to more efficient and more accurate reachable set computa-tions