Probabilistic and Randomized Methods for Design under Uncertainty
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In many engineering design and optimisation problems, the presence of uncertainty in the data is a central and critical issue. Different fields of engineering use different ways to describe this uncertainty and adopt a variety of techniques to devise designs that are at least partly insensitive or robust to uncertainty.Probabilistic and Randomized Methods for Design under Uncertainty examines uncertain systems in control engineering and general decision or optimisation problems for which data is not known exactly. Gathering contributions from the world’s leading researchers in optimisation and robust control; this book highlights the interactions between these two fields, and focuses on new randomised and probabilistic techniques for solving design problems in the presence of uncertainty:Part I describes general theory and solution methodologies for probability-constrained and stochastic optimization problems, including chance-constrained optimisation, stochastic optimization and risk measures;Part II focuses on numerical methods for solving randomly perturbed convex programs and semi-infinite optimisation problems by probabilistic techniques such as constraint sampling and scenario-based optimisation;Part III details the theory and applications of randomised techniques to the analysis and design of robust control systems.Probabilistic and Randomized Methods for Design under Uncertainty will be of interest to researchers, academics and postgraduate students in control engineering and operations research as well as professionals working in operations reasearch who are interested in decision-making, optimisation and stochastic modelling.
1Scenario approximations of chance constraints32Optimization models with probabilistic constraints493Theoretical framework for comparing several stochastic optimization approaches994Optimization of risk measures1195Sampled convex programs and probabilistically robust design1616Tetris : a study of randomized constraint sampling1897Near optimal solutions to least-squares problems with stochastic uncertainty2038The randomized ellipsoid algorithm for constrained robust least squares problems2239Randomized algorithms for semi-infinite programming problems24310A learning theory approach to system identification and stochastic adaptive control26511Probabilistic design of a robust controller using a parameter-dependent Lyapunov function30312Probabilistic robust controller design : probable near minimax value and randomized algorithms31713Sampling random transfer functions33114Nonlinear systems stability via random and quasi-random methods36515Probabilistic control of nonlinear uncertain systems38116Fast randomized algorithms for probabilistic robustness analysis415
