Robust Parameter Estimation for Linear Models with Set-membership Uncertainty

Abstract In this paper we address the problem of parameter estimation of a linear model y = A λ + ρ where the input matrix A is known and the additive uncertainty ρ is assumed to be unknown but bounded in an l ∞ norm by a given constant ∊. In this case for given data y the set of all admissible parameters λ consistent with the given model equation and the bound ϵ is a convex polytope. In this paper we attempt to estimate optimally, in the sense of maximizing the volume, a rectangular box which is guaranteed to lie completely inside the true region. The inner bounding region obtained in this way can be used together with an outer bounding region, in order to approximate as closely as possible the boundary of the actual admissible parameter polytope. A computable algorithm, using linear programming, is proposed and some numerical results are given to illustrate the behavior of the technique.