In this paper a new approach for fixed-structure H2 controller design in terms of solutions to a set of linear matrix inequalities are given. Both discreteand continuous-time single-input single-output (SISO) timeinvariant systems are considered. Then the results are extended to systems with polytopic uncertainty. The presented methods are based on an inner convex approximation of the non-conve...

Abstract: We introduce a new model for robust combinatorial optimization where the uncertain parameters belong to the image of multifunctions of the problem variables. In particular, we study the variable budgeted uncertainty, an extension of the budgeted uncertainty introduced by Bertsimas and Sim. Variable budgeted uncertainty can provide the same probabilistic guarantee as the budgeted uncer...

A new approach for robust fixed-order H∞ controller design by convex optimization is proposed. Linear timeinvariant single-input single-output systems represented by a finite set of complex values in the frequency domain are considered. It is shown that the H∞ robust performance condition can be approximated by a set of linear or convex constraints with respect to the parameters of a linearly p...

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

This paper is devoted to the problem of estimation of parameters for linear multioutput models with uncertain regressors and additive noise. The uncertainty is assumed to be described by intervals. Outer-bounding interval approximations of the non-convex feasible parameter set for uncertain system are obtained. The proposed method is based on the calculation of the interval solution for an inte...

We consider a two-period life-cycle model where uncertainty about future labour income is modelled by a fuzzy set. Applying a defuzzification strategy that explicitly takes the individual’s behaviour towards risk into account, we show that pessimistic individuals engage in precautionary savings even if marginal utility is not convex, e.g. in case of a quadratic utility function.  2001 Elsevier...

In this paper, we study the first application of robust and adaptive optimization in the Air Traffic Flow Management (ATFM) problem. The existing models for networkwide ATFM assume deterministic capacity estimates across airports and sectors without taking into account the uncertainty in capacities induced by weather. We introduce a weather-front based approach to model the uncertainty inherent...

For a mapping, fuzzy sets obtained by Zadeh's extension principle are images of other fuzzy sets on the domain of the mapping under the mapping. Some relationships between images of level sets of one or two fuzzy sets under a mapping and another fuzzy set obtained from the one or two fuzzy sets by Zadeh's extension principle are known. In the present paper, the known results are extended to mor...

In this article, a probabilistic fusion concept for road extraction from multi-aspect SAR images, which incorporates sensor geometry and context information, is proposed. Before fusion, the uncertainty of each extracted line segment is assessed by means of Bayesian probability theory. This assessment is performed on attribute-level and is based on predefined probability density functions learne...