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International audience; Least-Squares Support Vector Machines (LS-SVMs), originating from Statistical Learning and Reproducing Kernel HilbertSpace (RKHS) theories, represent a promising approach to identify nonlinear systems via nonparametric estimation of theinvolved nonlinearities in a computationally and stochastically attractive way. However, application of LS-SVMs and otherRKHS variants in the identification context is formulated as a regularized linear regression aiming at the minimization of the ℓ2loss of the prediction error. This formulation corresponds to the assumption of an auto-regressive noise structure, which is oftenfound to be too restrictive in practical applications. In this paper, Instrumental Variable (IV) based estimation is integratedinto the LS-SVM approach, providing, under minor conditions, consistent identification of nonlinear systems regarding thenoise modeling error. It is shown how the cost function of the LS-SVM is modified to achieve an IV-based solution. Although,a practically well applicable choice of the instrumental variable is proposed for the derived approach, optimal choice of thisinstrument in terms of the estimates associated variance still remains to be an open problem. The effectiveness of the proposedIV based LS-SVM scheme is also demonstrated by a Monte Carlo study based simulation example.

Identification of linear parameter varying models is considered in this paper, under the assumption that both the output and the scheduling parameter measurements are affected by bounded noise. First, the problem of computing parameter uncertainty intervals is formulated in terms of nonconvex optimization. Then, on the basis of the analysis of the regressor structure, we present an ad hoc convex relaxation scheme for computing parameter bounds by means of semidefinite optimization.