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

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Applications of Randomized Algorithms,e first present an overview of some of the main areas where randomized methods have been successfully used. Subsequently, we provide a more detailed description of some selected applications, which include the computation of PageRank in the Google search engine, control design of UAVs (unmanned aeri

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0178-5354 mal control or robust control.Many examples facilitate the r.The presence of uncertainty in a system description has always been a critical issue in control. The main objective of .Randomized Algorithms for Analysis and Control of Uncertain Systems, with Applications .(Second Edition) is to introduc

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Probability Inequalities,nstead based on the laws of large numbers. Specifically, the chapter includes Markov, Chebychev and Hoeffding inequalities. The additive and multiplicative Chernoff bounds are subsequently derived and the sample complexity for estimation of extrema is also studied.

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Scenario Approach to Probabilistic Design, theory, however, is to derive a rigorous probabilistic reliability certificate for the obtained design. The fundamental results of scenario theory are presented, together with extensions pertaining to scenario optimization with violated constraints and relations between scenario optimization and chance-constrained optimization.

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Overview,lly very difficult to compute exactly, can be easily approximated by means of randomization..The chapter describes in detail the structure of the book, which can be roughly divided into six parts, and it includes a block diagram which explains various interconnections between these parts.

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Statistical Learning Theory,amilies of functions are considered, instead of a fixed function. The chapter formally studies the UCEM (uniform convergence of empirical means) property and the VC dimension in the context of the Vapnik–Chervonenkis theory. Extensions to the Pollard theory for continuous-valued functions are also discussed.