The parameters identification problem of a sum u(t)=∑\limitsNi=1aie(λi,t), \ t∈ [0,T], where N∈ IN, ai∈ ℜ and λi∈ Ω are unknown parameters, and Ω is a bounded open set of ℜn is…
Abstract
The parameters identification problem of a sum u(t)=∑\limitsNi=1aie(λi,t), \ t∈ [0,T], where N∈ IN, ai∈ ℜ and λi∈ Ω are unknown parameters, and Ω is a bounded open set of ℜn is discussed. For some choices of the function e, this problem is an ill‐posed problem in the classical optimisation methods sense, such as the non‐linear least squares. The identification of parameters N, ai and λi being equivalent to the search of the distribution ℓ=∑\limitsNi=1aiδλi in the dual space of E=C(¯Omega;), the method developed here consists in finding a weak approximation of ℓ in the sense of the metric of the weak‐* topology on closed spheres of E’. Finally, we will apply this method to the identification problem of a sum of exponentials.