Randomized Algorithms for Analysis and Control of Uncertain Systems

This book introduces readers to the fundamentals of probabilistic methods in the analysis and design of systems subject to deterministic and stochastic uncertainty. It provides tools for dealing with uncertainty in control systems.

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 introduce the reader to the fundamentals of probabilistic methods in the analysis and design of systems subject to deterministic and stochastic uncertainty. The approach propounded by this text guarantees a reduction in the computational complexity of classical control algorithms and in the conservativeness of standard robust control techniques. The second edition has been thoroughly updated to reflect recent research and new applications with chapters on statistical learning theory, sequential methods for control and the scenario approach being completely rewritten. Features:· self-contained treatment explaining Monte Carlo and Las Vegas randomized algorithms from their genesis in the principles of probability theory to their use for system analysis;· development of a novel paradigm for (convex and nonconvex) controller synthesis in the presence of uncertainty and in the context of randomized algorithms; · comprehensive treatment of multivariate sample generation techniques, including consideration of thedifficulties involved in obtaining identically and independently distributed samples;· applications of randomized algorithms in various endeavours, such as PageRank computation for the Google Web search engine, unmanned aerial vehicle design (both new in the second edition), congestion control of high-speed communications networks and stability of quantized sampled-data systems. Randomized Algorithms for Analysis and Control of Uncertain Systems (second edition) is certain to interest academic researchers and graduate control students working in probabilistic, robust or optimal control methods and control engineers dealing with system uncertainties.The present book is a very timely contribution to the literature. I have no hesitation in asserting that it will remain a widely cited reference work for many years.M. Vidyasagar

Will give the reader tools for dealing with uncertainty in control systems which are more advanced and flexible than either traditional optimal control or robust control Many examples facilitate the reader's understanding of the theory and applications of randomized methods for control systems The description of the Randomized Algorithms Control Toolbox (RACT) also facillitates the implementation of specific randomized algorithms for analysis and control Reduces the computational cost of high-quality control and the complexity of the algorithms involved making similar results achievable with less effort by the user Includes supplementary material: sn.pub/extras

Autorentext

Roberto Tempo is one of the next generation of "top brass" in the control research community. He is currently the director of research at the National Research Council of Italy. Like any leading academic, he has the usual "long-as-your-arm" string of publications, both in refereed journals and at conferences. This is his second book, the first being an edited volume Robustness in Identification and Control. He is a regular member of program committees for several IFAC, IEEE, IEE and EUCA (European Union Control Association) conferences including Conference on Decision and Control (of which he will be program chair when the conference joins with ECC in Seville 2005) and is a fellow of the IEEE. He has been Associate Editor of IEEE Transaction on Automatic Control and is at present the Deputy Editor-in-Chief of Automatica the most widely read and respected journal in the field of theoretical control. Giuseppe Calafiore is an up-and coming academic who has established a reputation on both sides of the Atlantic with frequent periods as a visiting scholar at both Stanford University and UC Berkeley.

Inhalt
Uncertainty and Robustness.- Probability and Robustness of Uncertain Systems.- Elements of Probability Theory.- Uncertain Linear Systems and Robustness.- Linear Robust Control Design.- Some Limits of the Robustness Paradigm.- Probabilistic Methods for Robustness.- Monte Carlo Methods.- Randomized Algorithms in Systems and Control.- Probability Inequalities.- Statistical Learning Theory and Control Design.- Sequential Algorithms for Probabilistic Robust Design.- Sequential Algorithms for LPV Systems.- Scenario Approach for Probabilistic Robust Design.- Random Number and Variate Generation.- Statistical Theory of Radial Random Vectors.- Vector Randomization Methods.- Statistical Theory of Radial Random Matrices.- Matrix Randomization Methods.- Applications of Randomized Algorithms.