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Cover Art
Author Gerdts, Matthias.

Title Optimal control of ODEs and DAEs / Matthias Gerdts.

Published Berlin ; Boston : De Gruyter, [2012]


Location Call No. Status
 UniM ERC  515.642 GERD    AVAILABLE
Physical description ix, 458 pages : illustrations (some colour) ; 24 cm.
Series De Gruyter textbook.
De Gruyter graduate.
De Gruyter textbook.
De Gruyter graduate.
Bibliography Includes bibliographical references and index.
Contents Machine generated contents note: 1.Introduction -- 1.1.DAE Optimal Control Problems -- 1.1.1.Perturbation Index -- 1.1.2.Consistent Initial Values -- 1.1.3.Index Reduction and Stabilization -- 1.2.Transformation Techniques -- 1.2.1.Transformation to Fixed Time Interval -- 1.2.2.Transformation to Autonomous Problem -- 1.2.3.Transformation of Tschebyscheff Problems -- 1.2.4.Transformation of L1-Minimization Problems -- 1.2.5.Transformation of Interior-Point Constraints -- 1.3.Overview -- 1.4.Exercises -- 2.Infinite Optimization Problems -- 2.1.Function Spaces -- 2.1.1.Topological Spaces, Banach Spaces, and Hilbert Spaces -- 2.1.2.Mappings and Dual Spaces -- 2.1.3.Derivatives, Mean-Value Theorem, and Implicit Function Theorem -- 2.1.4.Lp-Spaces, Wq,p-Spaces, Absolutely Continuous Functions, Functions of Bounded Variation -- 2.2.The DAE Optimal Control Problem as an Infinite Optimization Problem -- 2.3.Necessary Conditions for Infinite Optimization Problems --
Contents note continued: 2.3.1.Existence of a Solution -- 2.3.2.Conic Approximation of Sets -- 2.3.3.Separation Theorems -- 2.3.4.First Order Necessary Optimality Conditions of Fritz John Type -- 2.3.5.Constraint Qualifications and Karush-Kuhn-Tucker Conditions -- 2.4.Exercises -- 3.Local Minimum Principles -- 3.1.Problems without Pure State and Mixed Control-State Constraints -- 3.1.1.Representation of Multipliers -- 3.1.2.Local Minimum Principle -- 3.1.3.Constraint Qualifications and Regularity -- 3.2.Problems with Pure State Constraints -- 3.2.1.Representation of Multipliers -- 3.2.2.Local Minimum Principle -- 3.2.3.Finding Controls on Active State Constraint Arcs -- 3.2.4.Jump Conditions for the Adjoint -- 3.3.Problems with Mixed Control-State Constraints -- 3.3.1.Representation of Multipliers -- 3.3.2.Local Minimum Principle -- 3.4.Summary of Local Minimum Principles for Index-One Problems -- 3.5.Exercises -- 4.Discretization Methods for ODEs and DAEs --
Contents note continued: 4.1.Discretization by One-Step Methods -- 4.1.1.The Euler Method -- 4.1.2.Runge-Kutta Methods -- 4.1.3.General One-Step Method -- 4.1.4.Consistency, Stability, and Convergence of One-Step Methods -- 4.2.Backward Differentiation Formulas (BDF) -- 4.3.Linearized Implicit Runge-Kutta Methods -- 4.4.Automatic Step-size Selection -- 4.5.Computation of Consistent Initial Values -- 4.5.1.Projection Method for Consistent Initial Values -- 4.5.2.Consistent Initial Values via Relaxation -- 4.6.Shooting Techniques for Boundary Value Problems -- 4.6.1.Single Shooting Method using Projections -- 4.6.2.Single Shooting Method using Relaxations -- 4.6.3.Multiple Shooting Method -- 4.7.Exercises -- 5.Discretization of Optimal Control Problems -- 5.1.Direct Discretization Methods -- 5.1.1.Full Discretization Approach -- 5.1.2.Reduced Discretization Approach -- 5.1.3.Control Discretization -- 5.2.A Brief Introduction to Sequential Quadratic Programming --
Contents note continued: 5.2.1.Lagrange-Newton Method -- 5.2.2.Sequential Quadratic Programming (SQP) -- 5.3.Calculation of Derivatives for Reduced Discretization -- 5.3.1.Sensitivity Equation Approach -- 5.3.2.Adjoint Equation Approach: The Discrete Case -- 5.3.3.Adjoint Equation Approach: The Continuous Case -- 5.4.Discrete Minimum Principle and Approximation of Adjoints -- 5.4.1.Example -- 5.5.An Overview on Convergence Results -- 5.5.1.Convergence of the Euler Discretization -- 5.5.2.Higher Order of Convergence for Runge-Kutta Discretizations -- 5.6.Numerical Examples -- 5.7.Exercises -- 6.Real-Time Control -- 6.1.Parametric Sensitivity Analysis and Open-Loop Real-Time Control -- 6.1.1.Parametric Sensitivity Analysis of Nonlinear Optimization Problems -- 6.1.2.Open-Loop Real-Time Control via Sensitivity Analysis -- 6.2.Feedback Controller Design by Optimal Control Techniques -- 6.3.Model Predictive Control -- 6.4.Exercises -- 7.Mixed-Integer Optimal Control --
Contents note continued: 7.1.Global Minimum Principle -- 7.1.1.Singular Controls -- 7.2.Variable Time Transformation Method -- 7.3.Switching Costs, Dynamic Programming, Bellman's Optimality Principle -- 7.3.1.Dynamic Optimization Model with Switching Costs -- 7.3.2.A Dynamic Programming Approach -- 7.3.3.Examples -- 7.4.Exercises -- 8.Function Space Methods -- 8.1.Gradient Method -- 8.2.Lagrange-Newton Method -- 8.2.1.Computation of the Search Direction -- 8.3.Exercises.
Subject Control theory -- Mathematical models.
Mathematical optimization.
ISBN 9783110249958 (alk. paper)
3110249952 (alk. paper)