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## Details

Genre/Form: | Electronic books |
---|---|

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Werner H Schmidt; Knut Heier; Leonhard Bittner; Roland Bulirsch |

ISBN: | 9783034888028 3034888023 |

OCLC Number: | 840291159 |

Description: | 1 online resource. |

Contents: | On the Convexification of Optimal Control Problems of Flight Dynamics -- Restricted Optimal Transportation Flows -- Relaxation Gaps in Optimal Control Processes with State Constraints -- Optimal Shape Design for Elliptic Hemivariational Inequalities in Nonlinear Elasticity -- A Discretization for Control Problems with optimality test -- Smooth and Nonsmooth Optimal Lipschitz Control -- a Model Problem -- Suboptimality Theorems in Optimal Control -- A Second Order Sufficient Condition for Optimality in Nonlinear Control -- the Conjugate Point Approach -- Extremal Problems for Elliptic Systems -- Existence Results for Some Nonconvex Optimization Problems Governed by Nonlinear Processes -- Multiobjective Optimal Control Problems -- Existence Principles and the Theory of Extremal Problems -- Hamilton-Jacobi-Bellman Equations and Optimal Control -- Output Target Control and Uncertain Infinite-Dimensional Systems -- Sensitivity Analysis of Stiff and Non-stiff Initial-value Problems -- Algorithm of Real-Time Minimization of Control Norm for Incompletely Determined Linear Control Systems -- Set-valued Calculus and Dynamic Programming in Problems of Feedback Control -- Strong Observability of Time-dependent Linear Systems -- Sensitivity Analysis and Real-Time Control of Nonlinear Optimal Control Systems via Nonlinear Programming Methods -- Accelerating Multiple Shooting for State-constrained Trajectory Optimization Problems -- SQP Methods and their Application to Numerical Optimal Control -- Predictor-Corrector Continuation Method for Optimal Control Problems -- Time Invariant Global Stabilization of a Mobile Robot -- Competitive Running on a Hilly Track -- Convex Domains of Given Diameter with Greatest Volume -- Isoperimetric and Isodiametric Area-minimal Plane Convex Figures -- Minimizing the Noise of an Aircraft during Landing Approach -- Real-Time Computation of Strategies of Differential Games with Applications to Collision Avoidance -- The Use of Screening for the Control of an Endemic Disease -- Optimal Control of Sloshing Liquids -- Free Surface Waves in a Wave Tank -- Efficient Convexification of Flight Path Optimization Problems -- Determining the Controllability Region for the Re-entry of an Apollo-type Spacecraft. |

Series Title: | International series of numerical mathematics, 124. |

Responsibility: | edited by Werner H. Schmidt, Knut Heier, Leonhard Bittner, Roland Bulirsch. |

### Abstract:

Variational Calculus, Optimal Control and Applications was the topic of the 12th Baltic Sea conference, traditionally an important meeting place for scientists from Eastern and Western Europe as well as the USA. This work contains contributions presented at that conference and addresses four problem complexes mostly motivated by practical problems. The starting points are often questions taken from flight dynamics. The first chapter deals with existence theory and optimality conditions needed for justification of, and used in, numerical algorithms. Analysis and synthesis of control systems and dynamic programming are presented in the second chapter. A modern interpretation of a solution of the Hamilton-Jacobi-Bellman equation is given. This is closely connected to the question of real-time or feedback control. Recent advances in the field of numerical methods and their applications to flight path optimization and fluid dynamics follow. The reader will find nonlinear programming methods, accelerated multiple shooting, homotopy and SQP methods. A wide variety of applications to mechanical and aerospace systems concludes this work: space flight problems, mobile robot controlling, geometrical extremal problems, fluid transport, fluid waves and human sciences.

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