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- Giuseppe Carlo Calafiore, Marco C. Campi
- Math. Program.
- 2005

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)

- Giuseppe Carlo Calafiore, Marco C. Campi
- IEEE Trans. Automat. Contr.
- 2006

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)

- Zheng-Hua Luo, Bao-Zhu Guo, +25 authors Fabrizio Dabbene
- 2004

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)

- Giuseppe Carlo Calafiore
- SIAM Journal on Optimization
- 2010

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 paper, we discuss linear programs in which the data that specify the constraints are subject to random uncertainty. A usual approach in this setting is to enforce the constraints up to a given level of probability. We show that, for a wide class of probability distributions (namely, radial distributions) on the data, the probability constraints can… (More)

- Laurent El Ghaoui, Giuseppe Carlo Calafiore
- IEEE Trans. Automat. Contr.
- 2001

This note presents a new approach to finite-horizon guaranteed state prediction for discrete-time systems affected 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 confidence ellipsoid for the state,… (More)

- Giuseppe Carlo Calafiore, Boris T. Polyak
- IEEE Trans. Automat. Contr.
- 2001

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

- Giuseppe Carlo Calafiore, Marina Indri, Basilio Bona
- J. Field Robotics
- 2001

Advanced robot control schemes require an accurate knowledge of the dynamic parameters of the manipulator. This article examines various issues related to robot dynamic calibration, from generation of optimal excitation trajectories to data acquisition and filtering, and experimental inertial and friction parameter estimation. In particular, a new method is… (More)

- Giuseppe Carlo Calafiore, Fabrizio Dabbene, Roberto Tempo
- IEEE Trans. Automat. Contr.
- 2000

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)

- Giuseppe Carlo Calafiore
- IEEE Trans. Systems, Man, and Cybernetics, Part A
- 2002

This paper discusses the problem of approximating data points in -dimensional Euclidean space using spherical and ellipsoidal surfaces. A closed form solution is provided for spherical approximation, while an efficient, globally optimal solution for the ellipsoidal problem is proposed in terms of semidefinite programming (SDP). In addition, the paper… (More)