Ebook: Probabilistic and Randomized Methods for Design under Uncertainty

In many engineering design and optimization 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 optimization problems for which data is not known exactly. Gathering contributions from the world’s leading researchers in optimization 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 optimization, stochastic optimization and risk measures;
• Part II focuses on numerical methods for solving randomly perturbed convex programs and semi-infinite optimization problems by probabilistic techniques such as constraint sampling and scenario-based optimization;
• Part III details the theory and applications of randomized 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 research who are interested in decision-making, optimization and stochastic modeling.

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In many engineering design and optimization 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 optimization problems for which data is not known exactly. Gathering contributions from the world’s leading researchers in optimization 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 optimization, stochastic optimization and risk measures;
• Part II focuses on numerical methods for solving randomly perturbed convex programs and semi-infinite optimization problems by probabilistic techniques such as constraint sampling and scenario-based optimization;
• Part III details the theory and applications of randomized 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 research who are interested in decision-making, optimization and stochastic modeling.

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In many engineering design and optimization 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 optimization problems for which data is not known exactly. Gathering contributions from the world’s leading researchers in optimization 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 optimization, stochastic optimization and risk measures;
• Part II focuses on numerical methods for solving randomly perturbed convex programs and semi-infinite optimization problems by probabilistic techniques such as constraint sampling and scenario-based optimization;
• Part III details the theory and applications of randomized 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 research who are interested in decision-making, optimization and stochastic modeling.

Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Scenario Approximations of Chance Constraints....Pages 3-47
Optimization Models with Probabilistic Constraints....Pages 49-97
Theoretical Framework for Comparing Several Stochastic Optimization Approaches....Pages 99-117
Optimization of Risk Measures....Pages 119-157
Front Matter....Pages 159-159
Sampled Convex Programs and Probabilistically Robust Design....Pages 161-188
Tetris: A Study of Randomized Constraint Sampling....Pages 189-201
Near Optimal Solutions to Least-Squares Problems with Stochastic Uncertainty....Pages 203-221
The Randomized Ellipsoid Algorithm for Constrained Robust Least Squares Problems....Pages 223-242
Randomized Algorithms for Semi-Infinite Programming Problems....Pages 243-261
Front Matter....Pages 263-263
A Learning Theory Approach to System Identification and Stochastic Adaptive Control....Pages 265-302
Probabilistic Design of a Robust Controller Using a Parameter-Dependent Lyapunov Function....Pages 303-316
Probabilistic Robust Controller Design: Probable Near Minimax Value and Randomized Algorithms....Pages 317-329
Sampling Random Transfer Functions....Pages 331-363
Nonlinear Systems Stability via Random and Quasi-Random Methods....Pages 365-379
Probabilistic Control of Nonlinear Uncertain Systems....Pages 381-414
Fast Randomized Algorithms for Probabilistic Robustness Analysis....Pages 415-431
Back Matter....Pages 433-457

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In many engineering design and optimization 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 optimization problems for which data is not known exactly. Gathering contributions from the world’s leading researchers in optimization 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 optimization, stochastic optimization and risk measures;
• Part II focuses on numerical methods for solving randomly perturbed convex programs and semi-infinite optimization problems by probabilistic techniques such as constraint sampling and scenario-based optimization;
• Part III details the theory and applications of randomized 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 research who are interested in decision-making, optimization and stochastic modeling.

Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Scenario Approximations of Chance Constraints....Pages 3-47
Optimization Models with Probabilistic Constraints....Pages 49-97
Theoretical Framework for Comparing Several Stochastic Optimization Approaches....Pages 99-117
Optimization of Risk Measures....Pages 119-157
Front Matter....Pages 159-159
Sampled Convex Programs and Probabilistically Robust Design....Pages 161-188
Tetris: A Study of Randomized Constraint Sampling....Pages 189-201
Near Optimal Solutions to Least-Squares Problems with Stochastic Uncertainty....Pages 203-221
The Randomized Ellipsoid Algorithm for Constrained Robust Least Squares Problems....Pages 223-242
Randomized Algorithms for Semi-Infinite Programming Problems....Pages 243-261
Front Matter....Pages 263-263
A Learning Theory Approach to System Identification and Stochastic Adaptive Control....Pages 265-302
Probabilistic Design of a Robust Controller Using a Parameter-Dependent Lyapunov Function....Pages 303-316
Probabilistic Robust Controller Design: Probable Near Minimax Value and Randomized Algorithms....Pages 317-329
Sampling Random Transfer Functions....Pages 331-363
Nonlinear Systems Stability via Random and Quasi-Random Methods....Pages 365-379
Probabilistic Control of Nonlinear Uncertain Systems....Pages 381-414
Fast Randomized Algorithms for Probabilistic Robustness Analysis....Pages 415-431
Back Matter....Pages 433-457
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