A NOVEL APPROACH TO SET-MEMBERSHIP OBSERVER FOR SYSTEMS WITH UNKNOWN EXOGENOUS INPUTS

 Motivated by the increasing need to monitor safety-critical systems subject to uncer-
tainties, a novel set-membership approach is proposed to estimate the state of a dynamical
system with unknown-but-bounded exogenous inputs. By fully utilizing the system struc-
tural information, the proposed algorithm can address both computational efficiency and
estimation accuracy without requiring restrictive conditions on the system. Particularly,
the system is first decomposed into the strongly observable subsystem and the weakly un-
observable subsystem. To make full use of the subsystem’s properties, a set-membership
observer based on the unknown input observer and an ellipsoidal set-membership observer
are designed for the two subsystems, respectively. Then, the resulting set estimates from
each subsystem are fused and transformed to obtain the set estimate for the original system,
which is guaranteed to bound the actual system state. The conditions for the boundedness
of the proposed set estimate are discussed, and the proposed set-membership observer is also
tested numerically using illustrative examples.