Variational Calculus, Optimal Control and Applications : International Conference in Honour of L. Bittner and R. Klötzler, Trassenheide, Germany, September 23–27, 1996

The 12th conference on "Variational Calculus, Optimal Control and Applications" took place September 23-27, 1996, in Trassenheide on the Baltic Sea island of Use­ dom. Seventy mathematicians from ten countries participated. The preceding eleven conferences, too, were held in places of natural beauty throughout West Pomerania; the first time, in 1972, in Zinnowitz, which is in the immediate area of Trassenheide. The conferences were founded, and led ten times, by Professor Bittner (Greifswald) and Professor KlCitzler (Leipzig), who both celebrated their 65th birthdays in 1996. The 12th conference in Trassenheide, was, therefore, also dedicated to L. Bittner and R. Klotzler. Both scientists made a lasting impression on control theory in the former GDR. Originally, the conferences served to promote the exchange of research results. In the first years, most of the lectures were theoretical, but in the last few conferences practical applications have been given more attention. Besides their pioneering theoretical works, both honorees have also always dealt with applications problems. L. Bittner has, for example, examined optimal control of nuclear reactors and associated safety aspects. Since 1992 he has been working on applications in optimal control in flight dynamics. R. Klotzler recently applied his results on optimal autobahn planning to the south tangent in Leipzig. The contributions published in these proceedings reflect the trend to practical problems; starting points are often questions from flight dynamics. Front Matter....Pages I-XVIII Front Matter....Pages 1-1 On the Convexification of Optimal Control Problems of Flight Dynamics....Pages 3-14 Restricted Optimal Transportation Flows....Pages 15-20 Relaxation Gaps in Optimal Control Processes with State Constraints....Pages 21-29 Optimal Shape Design for Elliptic Hemivariational Inequalities in Nonlinear Elasticity....Pages 31-40 A Discretization for Control Problems with Optimality Test....Pages 41-52 Smooth and Nonsmooth Optimal Lipschitz Control — a Model Problem....Pages 53-60 Suboptimality Theorems in Optimal Control....Pages 61-68 A Second Order Sufficient Condition for Optimality in Nonlinear Control — the Conjugate Point Approach....Pages 69-78 Extremal Problems for Elliptic Systems....Pages 79-85 Existence Results for Some Nonconvex Optimization Problems Governed by Nonlinear Processes....Pages 87-96 Multiobjective Optimal Control Problems....Pages 97-106 Existence Principles and the Theory of Extremal Problems....Pages 107-118 Front Matter....Pages 119-119 Hamilton-Jacobi-Bellman Equations and Optimal Control....Pages 121-132 Output Target Control and Uncertain Infinite-Dimensional Systems....Pages 133-142 Sensitivity Analysis of Stiff and Non-Stiff Initial-Value Problems....Pages 143-152 Algorithm of Real-Time Minimization of Control Norm for Incompletely Determined Linear Control Systems....Pages 153-162 Set-valued Calculus and Dynamic Programming in Problems of Feedback Control....Pages 163-174 Strong Observability of Time-Dependent Linear Systems....Pages 175-182 Front Matter....Pages 183-183 Sensitivity Analysis and Real-Time Control of Nonlinear Optimal Control Systems via Nonlinear Programming Methods....Pages 185-196 Accelerating Multiple Shooting for State-Constrained Trajectory Optimization Problems....Pages 197-206 Front Matter....Pages 183-183 SQP Methods and their Application to Numerical Optimal Control....Pages 207-222 Predictor-Corrector Continuation Method for Optimal Control Problems....Pages 223-232 Front Matter....Pages 233-233 Time Invariant Global Stabilization of a Mobile Robot....Pages 235-240 Competitive Running on a Hilly Track....Pages 241-250 Convex Domains of Given Diameter with Greatest Volume....Pages 251-260 Isoperimetric and Isodiametric Area-minimal Plane Convex Figures....Pages 261-270 Minimizing the Noise of an Aircraft During Landing Approach....Pages 271-280 Real-Time Computation of Strategies of Differential Games with Applications to Collision Avoidance....Pages 281-290 The Use of Screening for the Control of an Endemic Disease....Pages 291-300 Optimal Control of Sloshing Liquids....Pages 301-310 Free Surface Waves in a Wave Tank....Pages 311-320 Efficient Convexification of Flight Path Optimization Problems....Pages 321-330 Determining the Controllability Region for the Re-Entry of an Apollo-Type Spacecraft....Pages 331-340 The 12th conference on "Variational Calculus, Optimal Control and Applications" took place September 23-27, 1996, in Trassenheide on the Baltic Sea island of UseƯ dom. Seventy mathematicians from ten countries participated. The preceding eleven conferences, too, were held in places of natural beauty throughout West Pomerania; the first time, in 1972, in Zinnowitz, which is in the immediate area of Trassenheide. The conferences were founded, and led ten times, by Professor Bittner (Greifswald) and Professor KlCitzler (Leipzig), who both celebrated their 65th birthdays in 1996. The 12th conference in Trassenheide, was, therefore, also dedicated to L. Bittner and R. Klotzler. Both scientists made a lasting impression on control theory in the former GDR. Originally, the conferences served to promote the exchange of research results. In the first years, most of the lectures were theoretical, but in the last few conferences practical applications have been given more attention. Besides their pioneering theoretical works, both honorees have also always dealt with applications problems. L. Bittner has, for example, examined optimal control of nuclear reactors and associated safety aspects. Since 1992 he has been working on applications in optimal control in flight dynamics. R. Klotzler recently applied his results on optimal autobahn planning to the south tangent in Leipzig. The contributions published in these proceedings reflect the trend to practical problems; starting points are often questions from flight dynamics 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.