TY  - JOUR
EP  - 172
ID  - eprints3474
VL  - 70
JF  - Automatica
UR  - http://www.sciencedirect.com/science/article/pii/S0005109816301017
Y1  - 2016///
AV  - public
TI  - A probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic bounding
SP  - 158
N2  - Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic setting by employing sets of probability measures. Inference in set-membership estimation is thus carried out by computing expectations with respect to the updated set of probability measures PP as in the probabilistic case. In particular, it is shown that inference can be performed by solving a particular semi-infinite linear programming problem, which is a special case of the truncated moment problem in which only the zeroth order moment is known (i.e., the support). By writing the dual of the above semi-infinite linear programming problem, it is shown that, if the nonlinearities in the measurement and process equations are polynomial and if the bounding sets for initial state, process and measurement noises are described by polynomial inequalities, then an approximation of this semi-infinite linear programming problem can efficiently be obtained by using the theory of sum-of-squares polynomial optimization. We then derive a smart greedy procedure to compute a polytopic outer-approximation of the true membership-set, by computing the minimum-volume polytope that outer-bounds the set that includes all the means computed with respect to P.
PB  - Elsevier
SN  - 0005-1098
A1  - Benavoli, Alessio
A1  - Piga, Dario
ER  -