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.

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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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