A unified framework for solving a general class of conditional and robust set-membership estimation problems

In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic Control (2014

Error bounds for conditional algorithms in restricted complexity set membership identification

4Restricted complexity estimation is a major topic in control-oriented identification. Conditional algorithms are used to identify linear finite-dimensional models of complex systems, the aim being to minimize the worst-case identification error. High computational complexity of optimal solutions suggests employing suboptimal estimation algorithms. The paper studies different classes of conditional estimators and provides results that assess the reliability level of suboptimal algorithms.nonenoneGarulli, Andrea; Kacewicz, B. Z.; Vicino, Antonio; Zappa, G.Garulli, Andrea; Kacewicz, B. Z.; Vicino, Antonio; Zappa, G