Titlebook: Randomized Algorithms for Analysis and Control of Uncertain Systems; With Applications Roberto Tempo,Giuseppe Calafiore,Fabrizio Dabbene Bo

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Monte Carlo Methods, Carlo method has been widely used for simulations of various physical and mathematical systems and has a very long history that began in 1949 with the seminal paper of Metropolis and Ulam. The name Monte Carlo probably originated from the famous casino in Monaco and reflects the random and repetiti

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Statistical Learning Theory,ed sample complexity. This theory provides a fundamental extension of the probability inequalities studied in Chap. . to the case when parameterized families of functions are considered, instead of a fixed function. The chapter formally studies the UCEM (uniform convergence of empirical means) prope

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Randomized Algorithms in Systems and Control,is of uncertain systems, which are based on the Monte Carlo methods previously studied. Various meta-algorithms for probabilistic performance verification and probabilistic worst-case performance are introduced. For control design, subsequent chapters, which are highlighted here, discuss in detail f

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Sequential Methods for Probabilistic Design,framework that encompasses most of the sequential algorithms for feasibility that appeared in the literature. In particular, under a convexity assumption in the design parameters, we develop stochastic approximation algorithms that return a so-called reliable design. The notions of probabilistic ora

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Learning-Based Probabilistic Design,sign of systems affected by uncertainty formulating a learning-based approach. In particular, we develop a randomized technique for solving a nonconvex semi-infinite optimization problem and compute the related sample complexity. A sequential algorithm which provides a solution to the same problem i

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Random Number and Variate Generation,ariate and multivariate cases. These methods can be traced back to the issue of generating uniform random numbers in the interval [0,1]. Subsequently, we study the problem of univariate random generation. In particular, we present some standard results regarding transformations between random variab

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