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This paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms. This includes the wide class of NP-hard control problems representable by means of parameter-dependent linear… (More)

Many engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or 'instance' parameter. A recently emerged successful paradigm for attacking these problems is robust optimization , where one seeks a solution which simultaneously satisfies all possible constraint instances. In practice,… (More)

Random convex programs (RCPs) are convex optimization problems subject to a finite number N of random constraints. The optimal objective value J * of an RCP is thus a random variable. We study the probability with which J * is no longer optimal if a further random constraint is added to the problem (violation probability, V *). It turns out that this… (More)

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Abstract—This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and… (More)

|This paper presents a new approach to nite-horizon guaranteed state prediction for discrete-time systems aaected by bounded noise and unknown-but-bounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the state-space matrices on the uncertain parameters. The main result is that a minimal conndence ellipsoid for the state,… (More)

—In this note, we discuss fast randomized algorithms for determining an admissible solution for robust linear matrix inequalities (LMIs) of the form (1) 0, where is the optimization variable and 1 is the uncertainty, which belongs to a given set 1 1 1. The proposed algorithms are based on uncertainty randomization: the first algorithm finds a robust… (More)

This paper addresses the problem of constructing reliable interval predictors directly from observed data. Differently from standard predictor models, interval predictors return a prediction interval as opposed to a single prediction value. We show that, in a stationary and independent observations framework, the reliability of the model (that is, the… (More)

The objective of this paper is twofold. First, the problem of generation of real random matrix samples with uniform distribution in structured (spectral) norm bounded sets is studied. This includes an analysis of the distribution of the singular values of uniformly distributed real matrices, and an eecient (i.e. polynomial-time) algorithm for their… (More)

In this paper, we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations. The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the S-procedure. This formulation leads to convex optimization problems that can be… (More)

This paper discusses distributed approaches for the solution of random convex programs (RCP). RCPs are convex optimization problems with a (usually large) number N of randomly extracted constraints; they arise in several applicative areas, especially in the context of decision under uncertainty, see [2, 3]. We here consider a setup in which instances of the… (More)