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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. Two main approaches are generally available to tackle constrained optimization problems in presence of uncertainty: robust optimization and chance-constrained optimization. Robust optimization is a(More)
Foreword The subject of control system synthesis, and in particular robust control, has had a long and rich history. Since the 1980s, the topic of robust control has been on a sound mathematical foundation. The principal aim of robust control is to ensure that the performance of a control system is satisfactory, or nearly optimal, even when the system to be(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)
In this note, we derive an exact expression for the expected probability V of constraint violation in a sampled convex program (see Calafiore and Campi in Math. 2006 for definitions and an introduction to this topic): V = expected number of support constraints 1 + number of constraints. This result (Theorem 2.1) is obtained using a simple technique based on(More)
—In recent years, there has been a growing interest in developing randomized algorithms for probabilistic robustness of uncertain control systems. Unlike classical worst case methods, these algorithms provide probabilistic estimates assessing, for instance , if a certain design specification is met with a given probability. One of the advantages of this(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)
In this paper, we discuss semideÿnite 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 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)