In order to enhance the performance of electromagnetic interference (EMI) filters, it is necessary to identify high-frequency parasitic elements of their passive components, mainly those related to the coupled inductors. Motivated by this issue, in this work a realistic high-frequency model is proposed for the coupled inductors. Actually, using interval analysis in particular the forward–backward contractor, a set-membership algorithm has been developed to estimate systematically the parasitic elements linked with the magnetic components. The main advantages of this algorithm compared to the fitting methods are the values of the estimated parameters are always positive and the corrupted data are taken into account. The comparison of the simulation results and the experimental data allows us to validate the proposed method.

The importance of uncertainties in system design has been discussed by many authors. In the literature, there are two ways to represent uncertainties: the statistical (or stochastic) approach and the deterministic approach. In the stochastic approach, the uncertainty is modeled by a random process with a known statistical property. In the deterministic approach, the uncertainty is assumed to belong to a set: a classical (crisp) set 1 or a fuzzy set 2. This chapter presents some popular families of sets with their advantages and weaknesses. In recent years, zonotopes are used more and more to represent uncertainties due to the flexibility, the reduced complexity and specially the efficient computation of linear transformations and Minkowski sums. Zonotopes are a special class of convex symmetric polytopes. The chapter also proposes an overview of the main properties of zonotopes.

This paper presents a new approach for guaranteed state estimation based on zonotopes for linear discrete-time multivariable systems with interval multiplicative uncertainties, in the presence of bounded state perturbations and noises. At each sample time, the presented approach computes a zonotope which contains the real system state. A P-radius-based criterion is minimized in order to decrease the size of the zonotope at each sample time and to obtain an increasingly accurate state estimation. The proposed approach allows one to efficiently handle the trade-off between the complexity of the computation and the accuracy of the estimation. An illustrative example is analyzed in order to highlight the advantages of the proposed state estimation technique.

Cet article propose l'elaboration d'une strategie de commande predictive robuste par retour de sortie pour des systemes lineaires discrets soumis a des incertitudes, en considerant egalement des contraintes sur l'etat et la commande. L'originalite de l'approche proposee provient de la combinaison d'une commande predictive robuste a base de tubes d'incertitudes et d'un observateur developpe a l'aide d'ensembles zonotopiques. L'observateur est construit en resolvant hors ligne un probleme d'optimisation de type inegalite lineaire matricielle. L'erreur d'estimation est bornee par une sequence d'ensembles zonotopiques non croissants. Le correcteur est concu en utilisant la commande predictive basee sur des tubes afin d'assurer la stabilite de la boucle fermee tout en respectant les contraintes sur l'etat et la commande. Un exemple numerique illustre au final la performance de l'approche proposee.

This paper proposes a methodology for guaranteed state estimation of multivariable linear discrete time systems in the presence of bounded disturbances and noises. A zonotopic outer approximation of the state estimation domain is computed based on the minimization of the P-radius associated to the zonotope. The proposed method leads to an off-line Polynomial Matrix Inequality (PMI) optimization problem. A sub-optimal solution of this problem is obtained using relaxation techniques. An illustrative example is analyzed in order to highlight the performance of the proposed algorithm.

Abstract This paper proposes a methodology for guaranteed state estimation of linear discrete-time systems in the presence of bounded disturbances and noises. This aims at computing an outer approximation of the state estimation domain represented by a zonotope. A new criterion is used to reduce the size of the zonotope at each sample time. An illustrative example is analyzed in order to highlight the advantages of the proposed algorithm.

This paper proposes an approach to deal with the problem of robust output feedback model predictive control for linear discrete-time systems subject to state and input constraints, in the presence of unknown but bounded disturbances and measurement noises. The estimation of the states is built using a zonotopic set-membership estimation. This set is time-decreasing and is computed off-line as the solution of a Linear Matrix Inequality optimization problem. The control law is designed by using tube-based model predictive control such that the closed-loop stability is guaranteed and the state and input constraints are fulfilled. The proposed methodology is illustrated through numerical simulations.