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Robust Solutions To Uncertain Semidefinite Programs
 SIAM J. OPTIMIZATION
, 1998
"... In this paper we consider semidefinite programs (SDPs) whose data depend on some unknown but bounded perturbation parameters. We seek "robust" solutions to such programs, that is, solutions which minimize the (worstcase) objective while satisfying the constraints for every possible value ..."
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Cited by 96 (8 self)
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In this paper we consider semidefinite programs (SDPs) whose data depend on some unknown but bounded perturbation parameters. We seek "robust" solutions to such programs, that is, solutions which minimize the (worstcase) objective while satisfying the constraints for every possible value of parameters within the given bounds. Assuming the data matrices are rational functions of the perturbation parameters, we show how to formulate sufficient conditions for a robust solution to exist as SDPs. When the perturbation is "full," our conditions are necessary and sufficient. In this case, we provide sufficient conditions which guarantee that the robust solution is unique and continuous (Hölderstable) with respect to the unperturbed problem's data. The approach can thus be used to regularize illconditioned SDPs. We illustrate our results with examples taken from linear programming, maximum norm minimization, polynomial interpolation, and integer programming.
Robust Solutions To Uncertain Semidefinite Programs
, 1998
"... In this paper we consider semidenite programs (SDPs) whose data depends on some unknownbutbounded perturbation parameters. We seek "robust" solutions to such programs, that is, solutions which minimize the (worstcase) objective while satisfying the constraints for every possible values ..."
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Cited by 78 (3 self)
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In this paper we consider semidenite programs (SDPs) whose data depends on some unknownbutbounded perturbation parameters. We seek "robust" solutions to such programs, that is, solutions which minimize the (worstcase) objective while satisfying the constraints for every possible values of parameters within the given bounds. Assuming the data matrices are rational functions of the perturbation parameters, we show how to formulate sufficient conditions for a robust solution to exist, as SDPs. When the perturbation is "full", our conditions are necessary and sufficient. In this case, we provide sufficient conditions which guarantee that the robust solution is unique, and continuous (Hölderstable) with respect to the unperturbed problems' data. The approach can thus be used to regularize illconditioned SDPs. We illustrate our results with examples taken from linear programming, maximum norm minimization, polynomial interpolation and integer programming.
Uncertainty propagation in dynamic systems: a pragmatic approach applied to an example from the physical sciences
"... We present an approach to uncertainty propagation in dynamic systems, exploiting information provided by related experimental results along with their models. 1 ..."
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We present an approach to uncertainty propagation in dynamic systems, exploiting information provided by related experimental results along with their models. 1
Nonlinear Predictive Control using Fuzzy Models and Semidefinite Programming
, 1999
"... The present paper presents the first steps towards a theory to build Robust Nonlinear Predictive Control based on Fuzzy Models. The main idea behind this theory is to write the Predictive Control Problem as a Robust Optimization problem and apply Semidefinite Programming to solve in a efficient way ..."
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The present paper presents the first steps towards a theory to build Robust Nonlinear Predictive Control based on Fuzzy Models. The main idea behind this theory is to write the Predictive Control Problem as a Robust Optimization problem and apply Semidefinite Programming to solve in a efficient way the optimization. The information about the plant behavior and its uncertainties will be provided by the Fuzzy Model. 1. Introduction The use of fuzzy models for nonlinear system identification and modeling is becoming more popular due to the possibility of extract "local" information about the dynamics of the system. Extensive studies and algorithms to generate dynamic models via inputoutput signals has been developed. Also the representation of locally linearized models in the form of a TakagiSugeno fuzzy model has shown its advantages in simplifying the design of nonlinear controllers. On the other hand, model based predictive control techniques has been used in the process control ind...