Benavoli, Alessio and Piga, Dario
A probabilistic interpretation of setmembership filtering: application to polynomial systems through polytopic bounding.
Automatica, 70.
pp. 158172.
ISSN 00051098
(2016)
Abstract
Setmembership estimation is usually formulated in the context of setvalued calculus and no probabilistic calculations are necessary. In this paper, we show that setmembership estimation can be equivalently formulated in the probabilistic setting by employing sets of probability measures. Inference in setmembership 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 semiinfinite 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 semiinfinite 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 semiinfinite linear programming problem can efficiently be obtained by using the theory of sumofsquares polynomial optimization. We then derive a smart greedy procedure to compute a polytopic outerapproximation of the true membershipset, by computing the minimumvolume polytope that outerbounds the set that includes all the means computed with respect to P.
Actions (login required)

Edit Item 