Probabilistic and Randomized Methods for Design under Uncertainty

In many engineering design and optimization problems, the presence of uncertainty in the data is a critical issue. There are different ways to describe this uncertainty and to devise designs that are partly insensitive or robust to it. This book examines uncertain systems in control engineering and general decision or optimization problems for which data is uncertain. Written by leading researchers in optimization and robust control; it highlights the interactions between these two fields. Part I describes theory and solution methods for probability-constrained and stochastic optimization problems; Part II focuses on numerical methods for solving randomly perturbed convex programs and semi-infinite optimization problems by probabilistic techniques; Part III details the theory and applications of randomized techniques to the analysis and design of robust control systems. It will interest researchers, academics and postgraduates in control engineering and operations research as well as professionals working in operations research.

No other monograph contains an up-to-date coverage of randomized and probabilistic methods in robust control and optimisation an emerging field Includes supplementary material: sn.pub/extras

Autorentext

Drs. Giuseppe Calafiore and Fabrizio Dabbene work at the Politecnico di Torino, Italy, where Dr. Calafiore is an associate professor and Dr. Dabbene is a research fellow. Dr. Calafiore is an associate editor of IEEE Transactions on Systems, Man and Cybernetics and Dr. Dabbene is an associate editor of the conference editorial board of the IEEE Control Systems Society. Dr. Calafiore has published 60+ journal papers and both editors are co-authors of *Randomized Algorithms for Analysis and Control of Uncertain Systems (*Tempo, Calafiore and Dabbene, Springer-Verlag London, 2004).

In this edited work, Calafiore and Dabbene have brought together contributions from the world's leading experts in randomised methods as applied to robust design from both control and optimisation angles. The selection of authors is fully international and includes 15 from the United States.

Inhalt
Chance-Constrained and Stochastic Optimization.- Scenario Approximations of Chance Constraints.- Optimization Models with Probabilistic Constraints.- Theoretical Framework for Comparing Several Stochastic Optimization Approaches.- Optimization of Risk Measures.- Robust Optimization and Random Sampling.- Sampled Convex Programs and Probabilistically Robust Design.- Tetris: A Study of Randomized Constraint Sampling.- Near Optimal Solutions to Least-Squares Problems with Stochastic Uncertainty.- The Randomized Ellipsoid Algorithm for Constrained Robust Least Squares Problems.- Randomized Algorithms for Semi-Infinite Programming Problems.- Probabilistic Methods in Identification and Control.- A Learning Theory Approach to System Identification and Stochastic Adaptive Control.- Probabilistic Design of a Robust Controller Using a Parameter-Dependent Lyapunov Function.- Probabilistic Robust Controller Design: Probable Near Minimax Value and Randomized Algorithms.- Sampling Random Transfer Functions.- Nonlinear Systems Stability via Random and Quasi-Random Methods.- Probabilistic Control of Nonlinear Uncertain Systems.- Fast Randomized Algorithms for Probabilistic Robustness Analysis.