9527672 Schaettler This U.S.-Polish Cooperative Research award is on "Variational Methods in the Control of Nonlinear Systems." The principal researchers are Dr. Heinz Schaettler of Washington University, and Drs. Andrej Nowakowski and Stanislaw Walczak of the Institute of Mathematics of Lodz University. The researchers will combine their expertise in optimal control theory in the area of field theory, the Dubovitskii-Milyutin method, and nonregular/abnormal optimization problems to develop a broad and comprehensive theory of sufficient conditions for optimality and optimal control problems. The notion of a field of extremals and/or dynamic programming provide the theoretical basis both from a classical viewpoint using generalizations of Hilbert's invariant integral as well as from a modern perspective in the context of solutions to the Hamilton-Jacobi-Bellman equation. They will investigate links between geometric properties of extremals and singularities of the value function. In particular, they will analyze the role optimal abnormal extremals play in the construction of a regular synthesis, viz., an optimal field of extremals. They will give special attention to control systems of Dirichlet type for which currently only limited necessary conditions for optimality are available. This research in applied mathematics fulfills the program objectives of bringing together leading experts in the U.S. and Poland to combine complementary efforts and capabilities in areas of strong mutual interest and competence on the basis of equality, reciprocity, and mutuality of benefit. ***
