Recursive state bounding by parallelotopes

Analysis of consensus protocols with bounded measurement errors

“…Under the assumption of unknown but bounded measurement errors, the feasible state set (i.e., the set of all states compatible with the bounds on the noise) is explicitly derived. This kind of sets naturally arise in the context of set-membership estimation theory, which was originally developed for dynamic system identification and filtering problems, to guarantee a worst-case bound in the estimation of the model parameters or of the state vector [15,16]. The evolution of the feasible state set is used to evaluate the agreement of the team.…”

Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies

“…To implement such an algorithm, the set of uncertain states should be approximated since the exact set of estimated states would be difficult to compute. Several geometrical shapes have been proposed in the literature ranging from parallelotopes (Chisci et al, 1996) or ellipsoids (Maksarov and Norton, 1996) to zonotopes (Alamo et al, 2005). A zonotope X of order m can be viewed as the Minkowski sum of m segments:…”

“…An error-bounded state estimator assumes a priori bounds on noise and uncertain parameters and constructs sets of estimated states that are consistent with the a priori bounds and current measurements. Several researchers (Chisci et al, 1996;Maksarov and Norton, 1996;Shamma, 1997;Calafiore, 2001;Kieffer et al, 2002) have addressed this issue. Consider the system given by Eqn.…”

A set theoretic approach for time to contact estimation in dynamic vision

“…Recursive approximittion of polytopic regions through parallelotopes has been introduced in [19], and then applied to the state estimation problem in [6], where two sequences of outer approximating parallelotopes P ( k l k )…”

“…In order to reduce the conservativeness introduced by the approximation, minimum volume parallelotopes are considered. The measurements z, (u~, k ) contained in the vector yk are processed sequentially, so that the approximating boxes can be updated according to the ROBP Algorithm introduced in [6]. Hence, at time k , the set theoretic parallelotopic state filter provides the set estimate where is the central estimate of the state vector and Tklk defines the uncertainty region associated with the central estimate.…”