Optimal weighting design for distributed parameter systems estimation

This paper presents a method which aims at improving parameter estimation in dynamical systems. The general principle of the method is based on a modification of the least-squares objective function by means of a weighting operator, in view to improve the conditioning of the identification problem. First we recall a previous work using variational calculus in order to obtain the weighting operators through a linear equation. Then we propose a new approach which consists of determining the weights by formulating an optimization problem including positive semidefinite constraints (linear matrix inequalities, LMI).