Set Membership Parameter Estimation and Design of Experiments Using Homothety

In this note we address the problems of obtaining guaranteed and as good as possible estimates of system parameters for linear discrete–time systems subject to bounded disturbances. Some existing results relevant for the set–membership parameter identification and outer–bounding are first reviewed. Then, a novel method for characterizing the consistent parameter set based on homothety is offered; the proposed method allows for the utilization of general compact and convex sets for outer–bounding. Based on these results, we consider the one–step input design and identifiability problems in set–membership setting. We provide a guaranteed approach for the one–step input design problem, by selecting optimal inputs for the purpose of parameter estimation. As optimality criterion, the dimension and the outer– bounding volume of the “anticipated” consistent parameter set is considered. We furthermore derive a sufficient criterion for (one–step) parameter identifiability, i.e. when a point estimate for a parameter can be guaranteed for all possible measurements.